SOLUTION: The angle of depressions of a car on the ground from the top of a building is 72°.If the car is 200 feet away from the building.Find the height of the building?

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Question 1092478: The angle of depressions of a car on the ground from the top of a building is 72°.If the car is 200 feet away from the building.Find the height of the building?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the car and the building form a right triangle.

call this triangle ABC.

A is the lower left hand corner.
B is the upper left hand corner.
C is the lower right hand corner.

angle B is 72 degrees.
angle A is 90 degrees.
angle C is 18 degrees.

AC is equal to 200 feet.

you want to find the length of AB

tan(B) is equal to opposite / adjacent = 200 / AB

solve for AB to get AB = 200 / tan(B) = 200 / tan(72)

cot(C) is equal to adjacent / opposite = 200 / AB

solve for AB to get AB = 200 / cot(C) = 200 / cot(18)

you can use your calculator to solve.

200 / tan(72) = 64.98393925 feet.

200 / cot(18) = 200 / (1 / tan(18) = 200 * tan(18) = 64.98393925 feet.

either way you get AB = 64.98393925 feet.

you can also solve for the distance between the car and the top of the building.

that would be based on:

sin(B) = opp / hyp = 200 / BC

solve for BC to get BC = 200 / sin(B) = 200 / sin(72) = 210.2924448.

you have:

AB = 64.98393925
AC = 200
BC = 210.2924448

by pythagorus, BC^2 = AB^2 + AC^2

this becomes:

210.2924448^2 = 64.98393925^2 + 200^2

simplify to get 44222.91236 = 4222.91236 + 40000.

combine like terms to get 44222.91236 = 43222.91236

the formula is true and so the measurements of AB and AC and BC are true.

solution to your problem is that the height of the building is equal to 64.98393925 feet.

round as required.