Question

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

Answer 1

23°

Explanation:

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

`h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=√(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;

`(a)/(Sin \ A)=(b)/(Sin\ B)\\\\\\(76.15773)/(Sin \ 90)=(30)/(Sin\ h)\\\\h=Sin^(-1)(30)/(76.15773)\\\\=23.19859\approx 23\textdegree`

Hence, the angle of elevation is 23°