Question

if the angle of elevation of the sun is 60.9° when a building casts a shadow of 39.8 feet, what is the height of the building? round to at least the nearest tenth of a foot.

feet

question help: video written example

submit question

Explanation:

Step1: Set up tangent - ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 60.9^{\circ}$, the adjacent side to the angle of elevation is the length of the shadow ($x = 39.8$ feet), and the opposite side is the height of the building ($h$). So, $\tan(60.9^{\circ})=\frac{h}{39.8}$.

Step2: Solve for height $h$

Multiply both sides of the equation by 39.8: $h = 39.8\times\tan(60.9^{\circ})$.
We know that $\tan(60.9^{\circ})\approx1.788$. Then $h=39.8\times1.788 = 71.1624$.

Step3: Round the result

Rounding 71.1624 to the nearest tenth gives $h\approx71.2$.

Answer:

71.2