Question

A maple tree is 16 yards tall and its shadow is 12 yards long. A nearby observation tower is 12 yards tall. How long is the observation tower's shadow? Write your answer as a whole number or a decimal. Do not round.

Answer 1

Answer: 9 yards

Explanation:

Given

The maple tree is 16 yards tall and its shadow is 12 yards tall

Suppose the angle made by the maple tree is x

`\Rightarrow \cos x=(12)/(16)`

For the tower also, the angle made by the tower and its shadow is x

Suppose the length of the shadow is y

`\Rightarrow \cos x=(y)/(12)`

Substitute the value of
`\cos x`

`\Rightarrow (y)/(12)=(12)/(16)\\\\\Rightarrow y=9\ \text{yards}`