Question

A 6-foot tall man casts a shadow that is 12 feet long. What is the measure of the sun's angle of elevation? Enter your answer, rounded to the nearest degree, in the box.

Answer 1

Answer:

$27^{\circ}$

Step-by-step explanation:

Let x represent the sun's angle of elevation.

We have been given that a 6-foot tall man casts a shadow that is 12 feet long.

Upon looking at our attachment we can see that man and his shadow forma a right triangle with respect to ground, where height of man is opposite side and his shadow is adjacent side.

Since tangent relates opposite side of a right triangle with adjacent, so we can set an equation as:

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(x)=\frac{6}{12}$

$\text{tan}(x)=\frac{1}{2}$

Using arctan we will get,

$x=\text{tan}^{-1}(\frac{1}{2})$

$x=26.565051177078^{\circ}\approx 27^{\circ}$

Therefore, the measure of the sun's angle of elevation is 27 degrees.