Question

Find the angle of elevation of the sun when a 15.3 foot tall electric pole casts a 21.2 foot long shadow. Make a drawing, set up your trig ratio, and solve to the nearest tenth. Show work

Answer 1

To find the angle of elevation of the sun, set up the trigonometric ratio tangent using the height of the electric pole and the length of the shadow. Calculate the inverse tangent of the ratio to find the value of the angle.

Step-by-step explanation:

To find the angle of elevation of the sun, we can set up the trigonometric ratio tangent. Let's denote the angle of elevation as x. According to the problem, the opposite side is the height of the electric pole (15.3 ft) and the adjacent side is the length of the shadow (21.2 ft). So, we have:

tan(x) = opposite/adjacent = 15.3/21.2

Using a scientific calculator, we can find the inverse tangent of this ratio to find the value of x:

x = arctan(15.3/21.2)

Calculating this value gives x ≈ 37.6°. Therefore, the angle of elevation of the sun is approximately 37.6 degrees.