A 21-foot tree casts a 38-foot shadow directly down a slope when the angle of elevation of the sun is 32 degrees. Find theta, the angle of elevation of the ground (to the nearest tenth of a degree)

3.97°

Step-by-step explanation:

Let

θ = desired angle

α = 32° - θ = the angle above ground to the top of the slope

θ = 32° - a

If angle of the sun is 32° above a level horizon, then the angle at the top of the slope is given as δ = 90 - 32 = 58°. Now we can measure a

38/sin (58°) = 21/sin a

sin a = [21 sin (58°) ]/38

Sin a = 0.47

a = arcsin 0.47 = 28.03

Since,

θ = 32° - a

θ = 32° - 28.03° = 3.97°