Answer:
183.7 ft
Step-by-step 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
