Question

Sameena measures the angle from the ground to the top of a building from two locations. The angle of elevation from the first point is 45°, and the angle of elevation from the second point is 60°. The distance from the second point to the top of the building is 150 ft.

[Not drawn to scale]

What is the distance from the first observation point to the top of the tower (x)? Round the answer to the nearest tenth.
122.5 ft
183.7 ft
244.9 ft
501.9 ft

Answer 1

B: 183.7

Explanation:

First we need to find our values

A = 45°

B = 180 - 60 = 120

a = 150

Then we can solve for x using this formula x = a * sin(B)/sin(A).

x = 150 * sin(120)/sin(45)

x = 150 * √6/2

x = 75√6

x = 183.71173

Answer 2

183.7 ft

Explanation:

The mnemonic SOH CAH TOA reminds you that the relation between the hypotenuse and opposite side in a right triangle is ...

Sin = Opposite/Hypotenuse

For the first observation, the angle is 45° and the length of the hypotenuse of the triangle is given as x. For the second observation, the opposite side (building height) is the same, the angle is 60°, and the hypotenuse is 150 ft.

We can multiply the above equation by "Hypotenuse" to get an expression for "Opposite".

Opposite = Sin×Hypotenuse

For our two observations, this becomes ...

sin(45°)·x = (building height) = sin(60°)·(150 ft)

Dividing by the coefficient of x, we have ...

x = (150 ft)·sin(60°)/sin(45°) ≈ 183.7 ft