Question

J Pause If the sun is at an angle of 30 degrees from the horizontal and a tree casts a 15-meter shadow on the ground, which is the closest height of the tree? 30° 15 m 0 A 26.0 m OB. 8.7 m o C. 13.0 m O D. 7.5 m

Answer 1

Let us draw a figure to better understand the problem

From the trigonometric ratios, we know that

$\tan \theta=\frac{\text{opposite}}{\text{adjacent}}$

Let us substitute the given values and find the height (h) of the tree

$\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan (30\degree)=\frac{h}{15} \\ h=\tan (30\degree)\times15 \\ h=0.577\times15 \\ h=8.7\: m \end{gathered}$

Therefore, the height of the tree is closest to 8.7 m