Questions on Word Problems: Geometry answered by real tutors!

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Question 1055880: A tree with a circular base is to be cut down. If it takes one minute to cut 1', how long will it take to cut down a tree whose circular area is 121 square inches?
Click here to see answer by Fombitz(32388)

Question 1056406: the pool is 5m wide calculate its volume
b) a pump can drain water from the pool at 0.3m3/min how long does it take to drain the pool
Click here to see answer by ikleyn(52780)

Question 1056453: How many 0.75 foot long wooden planks must be laid end to end to cover a length of 7 1/2 yards??
Click here to see answer by Boreal(15235)

Question 1056513: if the side of a rhombus is 2cm what will be the length of its diagonals?

Click here to see answer by Edwin McCravy(20055)

Question 1056520: A living room of a house is 20.5 ft wide and 32.5 ft long. What is the approximate area of the room in square meters?
Click here to see answer by Alan3354(69443)

Question 1056613: The base of a dome is a circle with a diameter of 60m, with 2 parallel beams of 30m in length. Rounded to nearest decimal place, how far apart are the support beams.
Click here to see answer by ikleyn(52780)

Question 1056652: a polygon has n sides has n diagonals. What is n?
Click here to see answer by ikleyn(52780)

Question 1056695: A construction crew is building a straight ramp that rests on two beams. One beam is 3.5 feet tall and the other is 10.5 feet tall. The beams are 40 feet apart. What is the slope of the ramp?
Click here to see answer by Alan3354(69443)

Question 1056876: A field that is 3/4 acres must be planted with seeds of 36 people will spilt the job equally how many acres must each person have
Click here to see answer by Alan3354(69443)

Question 1056967: The question states: The vertices of triangle ABC are A(-5,3), B(2,2) and C(-1,-5). Which of the following is the length of the matrix from vertex B to side AC? I am told to find the mid point by computing as follows: (((-5 + -1)/2), (3+-5)/2). Why do I add -5 to -1 to get -6 instead of finding the distance between them to get -4?
Click here to see answer by ikleyn(52780)

Question 1057016: A rope of 18 metre is used to form a sector of a circle of radius 3.5 meter on a school Playfield. What is the size of the angle of the sector

Click here to see answer by Alan3354(69443)

Question 1057018: Two lines intersect to form a linear pair of congruent angles .The measure of one angle is (8x+10)� and the measure of the other angle is (15y/2)�.Find the values of x and y .
Click here to see answer by Alan3354(69443)

Question 1057059: A rectangular playing field with a perimeter of 100 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie?
Click here to see answer by ikleyn(52780)

Question 1057111: Find the radian measure of the largest angle in the triangle with side lengths of 77, 88, and 1313.
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Question 1057198: A triangular fence is being built to surround a garden. If two of the side lengths must be 4 feet and 12 feet, which inequality could be solved to determine the minimum length of the third side?
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Question 1057290: If y=12 when x=4,find when x=20
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Question 1057277: A triangular flower bed is to be enclosed by a small picket fence. If the base (b) of the triangle measures 40 feet minus the measure of its height (h), what height and base length will give the maximum area? what is the maximum area?
Click here to see answer by josgarithmetic(39617)

Question 1057289: A rancher has 600600 feet of fencing to put around a rectangular field and then subdivide the field into 33 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Click here to see answer by ikleyn(52780)

Question 1057341: the length of a Pole is measure as 5 meters to the nearest meter. what is the range of it's actual length. calculate the percentage error.
Click here to see answer by Fombitz(32388)

Question 1057377: in triangle ABC, the measure of angle B is twice the measure of angle A. the measure of angle C is 80 degrees more than that of angle A. find the measure of each angle.
Click here to see answer by ikleyn(52780)

Question 1057381: A triangular garden is enclosed by a fence. A dog is on a 5-m leash tethered to the fence at point P. One corner, B, of the fence is 6.5 m from P and forms a 41 degrees angle, as shown in the diagram. Determine the total length of fence that the dog can reach, to the nearest tenth of a metre, if the dog cannot reach side AC.
Click here to see answer by ikleyn(52780)

Question 1057467: Two adjcent walls of a 40 ft by 35 ft office are to be painted the walls are 8 ft high and include no doors or windows.
If each gallon of paint to be used covers 450 square feet how many gallons are needed
Click here to see answer by ikleyn(52780)

Question 1057572: A park designer wanted to place a fountain so that it was close to both the slide and the swings. Each unit on the grid represents 100ft. (a)Find the distance from the slide to the fountain. (b)Find the distance from the swings to the fountain. Show your work.

Click here to see answer by ikleyn(52780)

Question 1057574: The length of a rectangle is 4 inches more than the width. The area is 12 square inches. Find the dimensions.
Click here to see answer by ikleyn(52780)

Question 1057675: You are told that a triangle has sides that are 7 inches and 4 inches long. You were also told that the sides form an angle that measure 53�. Is there only one triangle that has these given dimensions why or why not.
Click here to see answer by addingup(3677)

Question 1057790: How many 1-inch-square floor tiles would cover this figure dimensions are in inches all angles are right angles.

Click here to see answer by Alan3354(69443)

Question 1057814: A portion of a track for a roller coaster is supported by two beams of different heights. The 40 foot and 30 foot beams are perpendicular to the ground. Steel cables are attached from the top of one beam to the bottom of the other beam. How far off the ground do the cables intersect?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1057845: A brace for a shelf has the shape of a right triangle. Its hypotenuse is 2020 inches long and the two legs are equal in length. How long are the legs of the triangle?

Click here to see answer by ikleyn(52780)

Question 1058022: You have a right triangle with hypotenuse 25. One of the legs gets decreased by 8 and other gets increased 4 and we still have a right triangle with hypotenuse 25. What are the lengths of the legs in the new triangle? (If you could tell me how you got your answer that would be helpful.)
Click here to see answer by josgarithmetic(39617)

Question 1058054: if I can do a job in 4 hours and we can do the same job in 2 hours, then how long can you do the same job alone?
Click here to see answer by Alan3354(69443)

Question 1058180: The perimeter of a rhombus is 40cm. If one diagnol is 16cm find (1) its another diagonal
Click here to see answer by ikleyn(52780)

Question 1056260: The length of a rectangle is 13 centimeters less than four times its width. Its area is 35 square centimeters. Find the dimensions of the rectangle.
Click here to see answer by addingup(3677)

Question 1058262: A certain blueprint shows two fences. Fence A is 1 1/4 yards long but is 1 1/2 inches long on the blueprint. What is the unit rate for inches per yard on this blueprint
Click here to see answer by josmiceli(19441)

Question 1058296: HOW TO SOLVE THE VALUES X AND Y?
Click here to see answer by ikleyn(52780)

Question 1058315: in an isosceles triangle the length of the equal sides is 2.5 times the length of the third side the perimeter is 10.8 m. Find the length of each side.
Click here to see answer by ikleyn(52780)

Question 1058418: There are 5shelves in a classroom cupboard each 234cm long. Each shelf is full of books 4.5 cm thick. How many bools are there altogther.

Click here to see answer by solve_for_x(190)

Question 1058429: A group of mountain climbers are using trigonometry to find the height of a mountain located in the Rockies. From point A, which is due west of the mountain, the angle of elevation to the top is 56 degrees. From point B, which is due east of the mountain, the angle of elevation to the top is 38 degrees. Points A and B are 9.4km apart. Determine the height of the mountain and round to the nearest meter.
This is what I have:
Triangle ABC-- base of triangle is line AB; top point C. Angle of A = 56 degrees, angle of B = 38 degrees, therefore angle C is 86 degrees. (38 + 56 - 180)
Using sine law to find the length of CB (aka "a") c= AB = 9.4km
a/sin A = c/sin C
a/sin(56) = 9.4/sin(86)
a= 9.4 sin(56)/ sin (86)
a= 7.8 km
Now drawing a line from C to AB and calling it h and thus making a right angle triangle I use sine ratio
sin (38)= opposite/hypotenuse
sin (38) = h/7.8
h= 7.8 sin(38)
h= 4.802km or 4802 meters.
Am I correct?
Click here to see answer by solver91311(24713)

Question 1058475: ONE SIDE OF A TRIANGLE IS HALF THE LONGEST SIDE. THE THIRD SIDE IS 16 FEET LESS THAN THE LONGEST SIDE. THE PERIMETER IS 69. FIND ALL THREE SIDES.

Click here to see answer by Cromlix(4381)

Question 1058499: There is a graphic of the function y=2x+1 (line) and a graphic of the function y=x2-2 (parabola). Find out the points of intersection of the two functions. Draw the graphics and show your calculations.
Click here to see answer by josgarithmetic(39617)

Question 1058531: A cottage under construction is to be 15.6m wide. The two sides of the roof are to be supported by equal rafters that meet at a 52 degree angle. Determine the length of the rafters to the nearest cm using
a) cosine law
b) sine law

Now, finding the answer with sine law was straightforward. Since sides b and c are equal the angles for B and C are also equal. 180 degrees - 52 degrees = 128/2 = 64 degrees for B and C.
Then use sine law to get a length of 17.8cm for either side.

Now with cosine law I am unsure. I've got three angles and a length....my textbook says I need either three lengths or two lengths and an angle in between them. I attempted anyway and this is what I got, without using the information provided by using sine law:

15.6^2 = x^2 + x^2 - 2(x)(x)cos(52)

243.36 = 2x^2 - 2x^2 cos(52)
And then I'm lost. Someone suggested these next steps:
243.36 = x^2 (2 - 2 cos(52))
x^2 = 243.36/0.769
x^2 = 316.463
x = sq root of 316.463 = 17.789 = 17.8
*Explain to me how that's legit. How did the right side of the equation turn from
2x^2 - 2x^2 cos (52)
into
x^2(2 - 2 cos(52)) ?
Thank You
Click here to see answer by Boreal(15235)

Question 1058536: On a day with no wind, a hot-air balloon hovers at a point above a long, straight river. On the west side of the balloon, a sailboat is spotted in the river at an angle of depression of 48 degrees. On the east side, a canoe spots the balloon at an angle of inclination of 29 degrees. The distance between the balloon and the canoe is 650m.

a) What is the height of the balloon?

b) What is the distance between the balloon and the sailboat?

c) What is the distance between the sailboat and the canoe?

My solutions:
Divide triangle BSC into two right angle triangles by drawing a line between angle B (the top) down to the base (line SC) and calling it h and the point where it meets SC as point D. Angle C
is 29 degrees, length BC is 650m, angle S is 48 degrees. Length BS is c.

a) Solving for h (height) sine theta in triangle BCD:

sin(29) = opposite/hypotenuse
sin(29) = h/650
h = 650sin(29)
h = 315.1 meters

b) sin(48) = opposite/hypotenuse in triangle BDS
sin(48) = 315.1/c
c = 315.1/sin(48)
c = 424 meters

c) finding length of SD
tan(48) = 315.1/SD
SD = 315.1/tan(48)
SD = 283.7

finding length DC
tan(29) = 315.1/DC
DC = 315.1/tan(29)
DC = 568.5

283.7 + 568.5 = distance between sailboat and canoe is 852.2 meters.

Am I right?

Click here to see answer by Boreal(15235)

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