Questions on Geometry: Triangles answered by real tutors!

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Question 751248: What is the perimeter and area of a 45°-45°-90° triangle with a hypotenuse length of 12 feet?

Answer by reviewermath(512)

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In a 45°-45°-90° triangle, the length of the hypotenuse is equal to sqrt%282%29

times the length of the leg.
If hypotenuse = 12 feet, then the length of each leg is 12%2Fsqrt%282%29

ft =

ft.
Perimeter = 12 + 2%286sqrt%282%29%29

ft =

ft
Area = Square the length of the leg then divide by 2
= %28%286sqrt%282%29%29%5E2%29%2F2

sq ft =

sq ft

Question 751141: find the perimeter and area of a square with diagonal length of 18 meters. give answer in simplest radical.
Answer by JoeTaxpayer(107)

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If the diagonal of the square is given, we use a^2+b^2=c^2 to get one side.
(But a=b for a square, so it's simply 2a^2)
2a^2=18^2
2a^2=324
a^2= 162 (Note - 162 = 81*2)
a= 9sqr(2) this is one side.
The area is a^2 or 162sq meters.
The perimeter is 4*9sqr(2) or 36sqr(2)

Question 751139: What is the perimeter and area of a 45°-45°-90° triangle with a hypotenuse length of 12 feet
Found 2 solutions by Cromlix, rfer:
Answer by Cromlix(307)   (Show Source):
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Using trigonometric ratios with
the right angle triangle.
Using cos = adjacent/hypotenuse
cos 45 = adjacent/12
Adjacent = 12*cos45 = 8.5 feet (1 decimal place)
Using sin = opposite/hypotenuse
sin45 = opposite/12
Opposite = 12*sin45 = 8.5 feet (1 decimal place)

Perimeter =
8.5 + 8.5 + 12 = 29 feet
Area of triangle = 1/2(b*h)
1/2(8.5*8.5)
= 36.1 ft^2
Hope this helps
:-)

Answer by rfer(12657)   (Show Source):
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=39 ft

Question 751143: To secure an outdoor canopy a 64 inch cord is extended from the top of a vertical pole to the ground. if the cord makes a 60 degree angle with the ground, how tall is the pole? give answer to the nearest tenth of an inch.
Answer by Cromlix(307)   (Show Source):
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Trigonometric ratio.
Imagine a right angle triangle
The pole represents the opposite side
The cord represents the hypotenuse.
Using sin = opposite/ hypotenuse
sin 60 = opposite/ 64 inches
Opposite = sin60 * 64 inches
Height of pole = 55.4 imches
Hope this helps
:-)

Question 750963: Find the base of an isosceles triangle if the perimeter is equal to 25 and the height is equal to 8.

Answer by tommyt3rd(513)   (Show Source):
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h=8-height
b-base
a-the isosceles sides
perimeter is 25 means:

and

or

so that

and thus after some algebra we get
b=369/50

:)

Question 750714: A perimeter of a parallogram is 72 inches and one side measures 12inches.what are the lengths in inches of otha 3sides?
Answer by Cromlix(307)   (Show Source):
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Perimeter = 2 lengths + 2 widths
If we take 2 of the sides to equal
2 x 12 inches = 24 inches, then the remaining two sides
must equal 48 inches. So by dividing by 2 gives 24 inches.
Therefore there are two 12 inch lengths and two 24 inch widths.

Question 750563: whats the value of x
Answer by Alan3354(30993)   (Show Source):
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whats the value of x
-----------
It varies.
It's a variable.

Question 750476: Two triangles are similar. The sides of the first triangle is 2,4,6. The largest side of the second triangle is 24. Find the perimeter of the second triangle.
Answer by stanbon(57299)   (Show Source):
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Two triangles are similar. The sides of the first triangle is 2,4,6. The largest side of the second triangle is 24. Find the perimeter of the second triangle.
----
Notice that the longest side is 3 times the shortest in the original triangle.
Notice that the middle side is 2 times the shortest in the original triangle.
------
The new triangle sides must be 8,16,24
The perimeter is 8+16+24 = 48
=====================
Cheers,
Stan H.

Question 750316: show that the points (a,0),(0,b) and 3a,-2b) lie on a straight line. find its equation
Answer by KMST(1868)   (Show Source):
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Two points determine a line.
We can calculate the slope of the line between 2 of those points.
From the slope and the coordinates of one of the points, we can get the equation of the line. If the coordinates of the third point satisfy that equation, the third point lies on that same line.
The slope of the line connecting (a,0) to (0,b) is

Since the y-intercept is at (0,b), b is the intercept, and we can write
as the slope-intercept form of the equation of the line connecting (a,0) to (0,b).
Substituting the x-coordinate of (3a,-2b) into the equation we can find if that point lies on the same line.
For , the point on the line has
so point (3a,-2b) lies on the same line as the other two points.

If we were not asked for the equation of the line, we could calculate the slopes for two different pairs of points. If we found the same slopes connecting two of the points with the other point, that would mean they all lie on the same line.

Question 749496: is 8 feet larger than 72 inches

Answer by timvanswearingen(103)   (Show Source):
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There are 12 inches in one foot:

There are 96 inches in 8 feet. So yes, 8 feet is larger than 72 inches.

Question 749516: 1. Find b. Round to the nearest whole inch.
the triangle ABC with length BC 14 in. Angle B = 82 degrees and Angle A= 54 degrees. And length AC = b
(Points : 1)
17 in.
6 in.
11 in.
14 in.

Answer by Alan3354(30993)   (Show Source):
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the triangle ABC with length BC 14 in. Angle B = 82 degrees and Angle A= 54 degrees. And length AC = b
-----------------
BC = a
-----------
a/sin(A) = b/sin(B)
14/sin(54) = b/sin(82)
b = 14*sin(82)/sin(54)
b =~ 17 in

Question 749486: consider triangle ABC, where the picture is here http://oi44.tinypic.com/xyge8.jpg
1. let ADF be the area of the triangle ADF, then

2. when BD=4 and CF=2, then BC=(B) and x satisfies the equation

solving this equation , we have
AD = (E)
solve for A,B,C,D, and E
Answer by lynnlo(4155)   (Show Source):
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Question 749435: I am looking at putting a camera in a 12x12 stall and the camera is 9 ft in the air. The camera I am looking at says it is a 63 degree angle. I need to know if that camera will cover the whole stall at that angle?
Thanks!
Answer by Alan3354(30993)   (Show Source):
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I am looking at putting a camera in a 12x12 stall and the camera is 9 ft in the air. The camera I am looking at says it is a 63 degree angle. I need to know if that camera will cover the whole stall at that angle?
--------------
12 by 12 must mean the floor of the stall.
What part is in the frame depends on the location relative to the floor and the focal length.
If it's above the center of the floor 9' up, and 63 degs is the included angle, it will cover a circle 5.52' in diameter. Not all of the floor.
------------
To view all of the floor, it would have to be 13.85' above it.

Question 749186: The area of a triangle is 20. The base is x+2 and the height is x what is the value of x
Answer by solver91311(16877)   (Show Source):
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The area of a triangle is the base times the height divided by 2, hence

Solve the quadratic. You will need the quadratic formula or, if you are a glutton for punishment, you can complete the square.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 749071: in a right-angled triangle one of the acute angles is 20 greater than then the other.fine the angles of the triangle
Found 2 solutions by Cromlix, solver91311:
Answer by Cromlix(307)   (Show Source):
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Angles in triangle:
x, x + 20 and 90.
Therefore:
x + (x + 20) + 90 = 180
2x + 110 = 180
2x = 180 - 110
2x = 70
x = 35 degrees
Therefore angles are:
35 degs, 55 degs and 90 degs

Answer by solver91311(16877)   (Show Source):
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The sum of the measures of the interior angles of any triangle is 180 degrees. Since a right triangle has one angle that measures 90 degrees, the sum of the measures of the two acute angles must be 180 minus 90 equals 90 degrees.

Solve for

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 748988: the height of a triangle measures 9 inches more then its base, the area is 45 square inches, the measures of the base and height of the triangle?how do i find
Answer by checkley79(3050)   (Show Source):
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AREA=BH/2
H=B+9
45=B(B+9)/2
45=(B^2+9B)/2 CROSS MULTIPLY.
45*2=B^2+9B
90=B^2+9B
B^2+9B-90=0
(B+15)(B-6)=0
B-6=0
B=6 ANS. FOR THE BASE.
H=6+9=15 ANS. FOR THE HEIGHT.
PROOF:
45=6*15/2
45=90/2
45=45

Question 749006: XYZ is an equileteral triangle of length 10cm. Find:
a) calculate the height if the triangle using pythagoras theorem.
b) calculate the area of the triangle
Answer by timvanswearingen(103)   (Show Source):
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The height would be drawn from a vertex to the midpoint of the opposite side. Setting up a right triangle and using the Pythagorean Theorem:

The height is:

Area is 1/2*base*height. The base is 10 and we just found the height:

Question 748353: gate is three feet wide and five feet high need to cut a board that fits diagonlly across. how long should the board be?
Answer by Alan3354(30993)   (Show Source):
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gate is three feet wide and five feet high need to cut a board that fits diagonlly across. how long should the board be?
---------
Use Pythagoras.

Question 748287: if the base of a right triangle measures 30 feet and the hypotenuse measures 45 feet, what is the hight of the triangle

Found 2 solutions by timvanswearingen, Cromlix:
Answer by timvanswearingen(103)   (Show Source):
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Use the Pythagorean Theorem:

Subtract 900 from both sides:

Take the square root of both sides:

This may need to be reduced with radicals or approximated to a decimal, whichever the problem requires.

Answer by Cromlix(307)   (Show Source):
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This is a Pythagoras question.
The triangle is lettered A,B,C
The base is BC and the hypotenuse is AC
The height is AB
AB^2 + BC^2 = AC^2
AB^2 = AC^2 - BC^2
AB^2 = 45^2 - 30^2
AB^2 = 2025 - 900
AB^2 = 1125
AB = square root of 1125
AB = 33.5 feet. (the height)

Question 748282: What is the value for X if there's 60 Degress and 6.9?
Answer by Alan3354(30993)   (Show Source):
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What is the value for X if there's 60 Degress and 6.9?
---------------
Where is x?

Question 748020: Find the area of a triangle where the base is 2 1/5 yards and the height is 5/7 yard. I know that a= 1/2 the product of its base and height.
The area is ___yd squared.
Answer by unlockmath(1599)   (Show Source):
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Hello,
We can multiply 2 1/5 * 5/7 * 1/2 by changing to this:
11/5 * 5/7 * 1/2 = 55/70 reduced to 11/14 square yards.
Make sense?
RJ
www.math-unlock.com

Question 747890: True or False :
An Altitude of an equilateral triangle is more than 1/3 the perimeter of the triangle.
Found 2 solutions by Alan3354, unlockmath:
Answer by Alan3354(30993)   (Show Source):
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True or False :
An Altitude of an equilateral triangle is more than 1/3 the perimeter of the triangle.
----------------
1/3 of the perimeter = one side.
The altitude is less than the side length.
False

Answer by unlockmath(1599)   (Show Source):
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False.
RJ

Question 747826: Please help me calculate the angle of an isoceles triangle in which each base angle is four times the vertical angle
Answer by Alan3354(30993)   (Show Source):
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Please help me calculate the angle of an isoceles triangle in which each base angle is four times the vertical angle
-----------
If by "vertical angle" you mean the angle and the vertex, then
the angles are x, 4x & 4x
----
The sum of the angles = 180 degs

Question 747388: In Triangle ABC, if angle A=60 degrees and angle B is greater than angle C, then the longest side is ?

Answer by tommyt3rd(513)   (Show Source):
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The sum of the measures of a triangle is 180 degrees. If the measure of angle B is greater than that of B and they must sum to 120 degrees, then the measure of B must exceed 60 and so it must be the greatest

Question 747341: find A, b, and c, 18 degrees, divided by 15
c I 18 degrees, and b is divided by 15
Answer by Alan3354(30993)   (Show Source):
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find A, b, and c, 18 degrees, divided by 15
c I 18 degrees, and b is divided by 15
-----------
idk what that means.

Question 747069: What is the hypotenuse of a triangle with one side that equals 120 and the other side equaling 150?
Answer by rfer(12657)   (Show Source):
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120^2+150^2=c^2
14400+22500=36900
sqrt 36900=192

Question 746890: A(1,2), B(-1,1), C(1,0), D(-1,0) and P is (t,0). (cordinates of p are located between 0 and 1 on axis X), we are to find the point P at which angle APB is maximized
tan(APC) is = 2/1-t, tan(BPD) = 1/1+t and hence tan(APC) = t+x/t^2+y
therefore, the cordinates of point P are (t,0)

Answer by solver91311(16877)   (Show Source):
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Let refer to angle APC. Let refer to angle APB. Our task is to maximize

is indeed , but you have a sign error or . Should be .

Using those values, and the fact that , you should be able to derive the fact that:

Use the quotient rule to find the derivative,

Set the numerator of the derivative equal to zero and solve the quadratic for the positive value for that yields a maximum tangent, and therefore a maximum angle.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 746928: A triangle has sides of lengths 6,12, and 15.find the measure of the smallest angle
Answer by Alan3354(30993)   (Show Source):
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A triangle has sides of lengths 6,12, and 15.find the measure of the smallest angle
----------------
The smallest angle is opposite the shortest side.
Use the Cosine Law.

Solve for the cosine, then the angle.

Question 746903: The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?

Answer by timvanswearingen(103)   (Show Source):
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Let x represent the length of the base.
Then the height can be represented as (5 units more than twice the base)
Now, the formula for the area of a triangle is
So,
Using the distributive property,

Subtract 21 from both sides,

Now, using a=1, b=5/2, and c=-21, plug into the quadratic formula.

There are two possible answers. or
The second answer would result in a negative number. Since we are trying to find out the length of the base of a triangle, we can throw out the negative answer.
Thus,
So x is about 3.925 units.
x was representing the base. Since the height was 2x+5, simply plug in the x value found above to find the height.

h=12.850 units

Question 746797: the perimeter of a triangle is 34. find the side lenghts of the triangle. the hypotenuse is x+3, the base is 3x-9 and the height is x
thank you :)
Answer by Cromlix(307)   (Show Source):
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Perimeter is a total of the 3 sides
(x + 3) + (3x - 9) + x
5x - 6 = 34
5x = 40
x = 8
base = 15
hypotenuse = 11
height = 8

Question 746794: Triangle ABC is a right triangle. Side AC has a length of 8M and side BC has a length of 4M. Find the length of side AB.
Answer by Cromlix(307)   (Show Source):
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I am assuming that your right angle is at B
AB^2 + BC^2 = AC^2
AB^2 = AC^2 - BC^2
AB^2 = (8)^2 - (4)^2
AB^2 = 64 - 16
AB = square root of 48
AB = 6.9 ( 1 decimal place)

Question 746756: In Triangle ABC, Angle B = 15 degrees less than twice angle A and Angle C is more than angle A. Find angle C.
Answer by tommyt3rd(513)   (Show Source):
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B=2A-15
C>A
and A+B+C=180
which becomes...
A+(2A-15)+C=180
C=180+15-3A
C=165-3A

so

Which sets our boundary to test for valid triangles. After trial and error (there's probably a better way) we can deduce the following.
The least value for C under these conditions is C=42 and the greatest is a little more than 142
so...these are pretty good approximations

Question 746755: The sum of the complement and the supplement of an angle is 186 degrees. Find the Angle.
Answer by tommyt3rd(513)   (Show Source):
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complement: 90-x
supplement: 180-x
so...

Question 746754: The sides of an equilatersl triangle are 3x-1, 5y, and x+13. Find the measures of each side.
Answer by tommyt3rd(513)   (Show Source):
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equilateral => 3x-1=x+13 => x=7
and x+7 turns into 7+13=20
and so all sides are 20 units

:)

Question 746547: Which is the smallest possible answer for an isosceles triangle, if one side is 18cm and your choices are

A:15cm
B:16cm
C:17cm
D:18cm
Answer by solver91311(16877)   (Show Source):
You can put this solution on YOUR website!

Your question does not make sense. Write the question exactly as it was presented to you -- and I know it wasn't written that way.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 743936: find the unknown length in the right triangle one side is 9m and the other side 15m
Answer by tommyt3rd(513)   (Show Source):
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If we assume that 15m is the longest side then a side of 12m will give us a right triangle (why?)
:)

Question 743747: In a right triangle with g the right angle, a = 69.2° and c = 28.3. What is b?
Answer by tommyt3rd(513)   (Show Source):
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so

b=10.05

Question 745829: Find the area of triangle ABC to the nearest tenth if necessary.
A= 35 degrees
b=3 ft
c= 7 ft
Answer by tommyt3rd(513)   (Show Source):
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the area is found immediately by the formula:

which when calculated gives: A=6.0 square feet (when you check make sure your calculator is in degree mode)
:)

Question 745638: is a triangle with angles that are 60 degrees unique? why or why not?
Answer by Alan3354(30993)   (Show Source):
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is a triangle with angles that are 60 degrees unique?
No
--------
why or why not?
There are an infinite # of possible side lengths.

Question 745646: how many diferent triangles can be drawn with only one 80 degree angle?
Answer by Alan3354(30993)   (Show Source):
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how many diferent triangles can be drawn with only one 80 degree angle?
--------------
It's not clear what you mean.
You can't make a triangle with only 1 angle, whatever the measure.
---
If you mean that one angle is 80 degs and the other 2 are not 80 degs, there's an infinite # of them.

Question 745633: is it possible to draw a triangle with a 90 degree angle with one side measures 4 inches and one measures 3 inches long?
Answer by tommyt3rd(513)   (Show Source):
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yes - the famous 3-4-5 triangle is a right triangle (it has an angle of 90 degrees)