Question

A tree casts a shadow that is 150 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30°, how tall is the tree to the nearest foot?

A) 75 feet

B) 87 feet

C) 106 feet

D) 212 feet

Answer 1

B) 87 feet

Explanation:

The mnemonic SOH CAH TOA reminds you the relationship between angle, adjacent, and opposite sides is ...

... Tan = Opposite/Adjacent

In this geometry, the side adjacent to the angle is marked 150 ft, and the side opposite the angle is the height we want to find. This means ...

... tan(30°) = height/(150 ft)

Multiplying by 150 ft, we get ...

... height = (150 ft)·tan(30°) ≈ 87 ft