Questions on Geometry: Triangles answered by real tutors!

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Question 146185: How do I know what kind of triangle it will form from it's length measurements? Acute, Right, or Obtuse?
1) 4cm, 4cm, 4cm
2) 3cm, 4cm, 5cm
3) 5cm, 11cm, 12cm
Click here to see answer by nabla(475)

Question 146298: Find the measure of the hypotenuse of a 30-60-90 triangle whose longer leg has a measure of 6 meters. Give answer in simplified radical form???
Click here to see answer by edjones(7569)

Question 146788: the perimeter of a rectangle is 234 meters. The width is 3 meters less than the length. Find the lenght and width.
Click here to see answer by BrittanyM(80)

Question 146790: the number(G) of gears a machine can make varies directly as the time(t) it operates. If it can make 2200 gears in 5 hours how many gears can it make in 8 hours?
Click here to see answer by Fombitz(13828)

Question 146806: Let A = (0,0), B = (4,2), C = (1,3), find the exact size of angle CAB. Justify your answer without your protractor.
Click here to see answer by Alan3354(30993)

Question 146950: THIS IS THE MOST IMPORTANT QUESTION ON MY HOMEWORK AND I JUST CAN'T FIGURE IT OUT!!! please help !
A 25 foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down by 4 feet, by how many feet will the bottom slide out?
Click here to see answer by scott8148(6628)

Question 147048: Pat and Chris were out in their row boat one day, and Chris spied a water lily. Knowing that Pat liked a mathmatical challenge, Chris announced that, with the help of the plant, it was possible to calculate the depth of the water under the boat. When pulled taut, the top of the plant was origionally 10 inches above the water surface. While Pat held the top of the plant, which remained rooted to the lake bottom, Chris gently rode the boat 5 feet. This forced Pat's hand to the water surface. Use this information to calculate the depth of the water.

(I tried finding the depth but I didn't know how to get the lengths. I know it has something to do with a triangle.
Click here to see answer by iNeed(3)

Question 147051: i have a triangle and one side is 28 ft., the other 25 ft. and i need to find the measurement of the third side which is also the longest side
Click here to see answer by iNeed(3)

Question 147089: I have been out of high school and college for over 4 years now...so I used to know the answer, but we are far from it now! I am looking for the "rules" or "formula" or "whatever" that makes this a correct statement. You have a triangle with a right angle. Side A =3ft Side B=4ft (side A and B are connected by the right angle). We know that side C (the hypotonus) =5ft. I want this equation in a larger term (ie Side A=10ft Side B=20ft what is side C) Thanks so much for your help! I actually miss doing this on a regular basis! I loved math in high school, and now it just helping my dad build a cabin. Thanks again. Michelle Wagner
Click here to see answer by jim_thompson5910(28595)

Question 147100: In Triangle ABC, it is given that CA=CB. Points P and Q are marked on segments CA and CB respectively, so that angles CBP and CAQ are the same size. Prove that CP=CQ.
Thank you.
Click here to see answer by Edwin McCravy(8909)

Question 147115: A Triancle is Isosceles if it has at least two sides that are congruent. if the vertices of a triangle are given as A (0,8), R (-4,5), and T (-1,1) determine if Triangle ART is Isosceles or not.
Click here to see answer by Alan3354(30993)

Question 146953: Consider the triangle defined by P=(1,3), Q=(2,5, and R=(6,5). The transformation defined by T(x,y)=(x+2,y-1) is mathematical notation for translating a point by the vector [2,-1]. The point P(1,3) becomes T(1,3)=(1=2,3-1)=P'(3,2). Find Q' and R'. Graph both the original triangle and its image.
Click here to see answer by psbhowmick(529)

Question 147275: given an arbitrary triangle,what can you say about the sum of 3 exterior angles, 1 for each vertex of the triangle??

thnx again
Click here to see answer by Earlsdon(6287)

Question 147277: Ive tried this problem 6 different times, and cannot seem to find the answer.

Given triangle ABC with AB = AC, extend segment AB to a point P so that B is between A and P and BP = BC. In the resulting triangle APC, show that angle ACP is exactly three times the size of angle APC. (By the way, notice that extending segment AB does NOT mean the same thing as extending segment BA.)
thnx!!!
Click here to see answer by vleith(2825)

Question 147274: If ABC is any triangle, and TAC is one of its exterior angles, then what can be said about the size of angle TAC, in relation to the other angles of the figure?
thanks !!!!!
Click here to see answer by vleith(2825)

Question 147268: PLEASE HELP! I don't know how to find the length of any altitude. There are several problems on my homework like this, so if i understand the steps for this problem, i can figure out the others. THANKS!

A triangle that has a 13-inch side, a 14-inch side, and a 15-inch side has an area of 84 square inches. Accepting this fact, find the lengths of all three altitudes of this triangle.

Click here to see answer by scott8148(6628)

Question 147271: If it is know that one pair of alternate interior angles is equal, what can be said about...
-the other pair of alternate interior angles
-either pair of alternate EXTERIOR angles
-any pair of corresponding angles
-either pair of non-alternate interior angles.

THANKS SO MUCH
Click here to see answer by Nate(3500)

Question 147336: Given isosceles triangle ABC where AB = BC = 10 and the altitude from B has length 4. Find the length of the base.

Thanks so much, I really don't understand altitude problems.
Click here to see answer by Nate(3500)

Question 147340: prove that the sum of the angles of any quadrilateral is 360 degrees.
does it have to do with the expression: (n-2)180
where n is the number of sides?
Click here to see answer by nabla(475)

Question 147468: Triangle ABC is isosceles with base AC. If AB=7x+3, CB=8x-9, and AC=5x+6, find the lengths of the sides of the triangle
Click here to see answer by jim_thompson5910(28595)

Question 147624: The second angle of a triangle is 4 times as large as the first. The third angle is 45 degrees less than the sum of the other two angles. Find the measurment of each angle.
Click here to see answer by mangopeeler07(462)

Question 147485: Triangle EWS has a perimeter of 26 and SE = 1/2 WE. The midsegment parallel to WS = 4. Find the lengths of the three sides of this triangle.
thank you soo much
Click here to see answer by aswathytony(47)

Question 147676: Find x.
If a triangle of known measurement is 45 degrees.
Click here to see answer by GKelly(4)

Question 147488: Let A = (1,1), B = (3,5), and C = (7,2). Explain how to cover the whole plane with non overlapping triangles, each of which is congruent to triangle ABC.
In the pattern of lines produced by your tessellation, you should see triangles of many different sizes. What can you say about their sizes and shapes?

please help me! i am stuck... again
Click here to see answer by mangopeeler07(462)

Question 147597: The midpoints of a triangle are (3,-1) (4,3) and (0,5). Find coordinates for the vertices of the triangle...
Click here to see answer by stanbon(57361)

Question 147768: A bell rope, passing through the ceiling above, just barely reaches the belfry floor. When one pulls the rope to the wall, keeping the rope taut, it reaches a point that is three inches above the floor. It is four feet from the wall to the rope when the rope is hanging freely. How high is the ceiling?

(I made a diagram, but I don't really understand what the bell rope and belfry floor is. My answer was approx. 3.4 feet, but that doesn't sound correct to me. I found it by using triangles with x, 2x, and x square root 3.)

Click here to see answer by stanbon(57361)

Question 147838: I got an answer for this, but I'm not sure if i'm right. thanks!!!!
Standing on a cliff 380 meters above the sea, Sue sees an approaching ship and measures its angle of depression, obtaining 9 degrees. How far from the shore is the ship?
Now Sue sights a second ship beyond the first. The angle of depression of the second ship is 5 degrees. How far apart are the 2 ships?

My answer was about 2399.226 meters away, and 1944.194 meters apart.
Click here to see answer by Fombitz(13828)

Question 147839: a 5 foot emma student casts an 8 foot shadow. how high is the sun in the sky? this is another way6 to ask the angle of elevation of the sun.

my answer was 32.0053821 degrees but i'm not sure if i'm right. thanks for the help!
Click here to see answer by Earlsdon(6287)

Question 147931: If the lengths of the sides of a triangle are integers and their product is 504, what is a possible perimeter of the triangle?
Click here to see answer by Fombitz(13828)

Question 147591: Trapezoid ABCD has parallel sides AB and CD, a right angle at D, and the lengths AB = 15. BC = 10. and CD = 7. find the lenghth DA.

thankks!
Click here to see answer by orca(409)

Question 148148: to the nearest tenth of a degree, how large are the congruent angles of an isosceles triangle that is exactly as tall as it is wide? (There is more than one interpretation.)
Click here to see answer by Alan3354(30993)

Question 148263: What is two sets of Pythagorean Triples that are similar in ratio to the triple 6,8,10.
Click here to see answer by Alan3354(30993)

Question 148268: Triangles ABC and DEF are similar
AB=5.0 cm
BC=6.0 cm
AC=7.0 cm
If triangle DEF has a perimeter of 360 degrees find the length of the sides of ABC
Click here to see answer by mangopeeler07(462)

Question 148267: Cos 30 degrees = Sin ??? degrees
Click here to see answer by mangopeeler07(462)

Question 148255: 2 triangles are similar
Triangle RTS where rt=4.2 and st=6.0 do not know rs
Triangle JLK where lk=8
what is the length of JL
Click here to see answer by Alan3354(30993)

Question 148385: Taylor lets out 20 meters of kite string then wonders how high the kite has risen. Taylor is able to calculate the answer after using a protractor to measure the 63-degree angle of elevation that the string makes with the ground. How high is the kite, to the nearest meter? What unrealistic assumptions did you make in answering this question?

thanks -cj
Click here to see answer by Earlsdon(6287)

Question 148390: if the sides of a triangle are 13, 14 and 15 cm long, then the altitude drawn to the 24 cm side is 12 cm long. how long are the other two altitudes?> which side has the longest altitude?
Click here to see answer by stanbon(57361)

Question 148414: In the right triangle ABC, AC= 12, angle B= 30 degrees, Angle C= 90 degrees, and Angle A= 60 degrees.
What is the perimeter of the Triangle
Click here to see answer by Alan3354(30993)

Question 148401: a right triangle has a 123 foot hypotenuse, and a 38 foot leg. to the nearest tenth of a degree, what are the sizes of its acute angles?
thank you
Click here to see answer by Alan3354(30993)

Question 148429: The vertices of a triangle lie in a coordinate plane at (2,1),(2,4),and (6,1)
What is the area of the triangle.
Click here to see answer by edjones(7569)

Question 148446: 10. If the sides of a triangle are 13, 14, and 15 cm long, then the altitude drawn to the 14-cm side is 12 cm long. How long are the other two altitudes? Which side has the longest altitude?

Click here to see answer by jim_thompson5910(28595)

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