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

Step-by-step 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

$\Rightarrow \cos x=\dfrac{12}{16}$

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

Suppose the length of the shadow is y

$\Rightarrow \cos x=\dfrac{y}{12}$

Substitute the value of $\cos x$

$\Rightarrow \dfrac{y}{12}=\dfrac{12}{16}\\\\\Rightarrow y=9\ \text{yards}$