Question

The sun casts a 70 foot shadow on a 30 foot tree. Find the angle of elevation to the nearest degree.

Answer 1

Answer:

23°

Step-by-step explanation:

We apply Pythagorean theorem to determine the missing length, Hypotenuse:

$h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=\sqrt{5800}\\\\=76.15773\ ft$

This hypotenuse corresponds to the right triangle and the tree's height, corresponds to the angle of elevation:

-We apply the law of Sines;

$\frac{a}{Sin \ A}=\frac{b}{Sin\ B}\\\\\\\frac{76.15773}{Sin \ 90}=\frac{30}{Sin\ h}\\\\h=Sin^{-1}\frac{30}{76.15773}\\\\=23.19859\approx 23\textdegree$

Hence, the angle of elevation is 23°