Mt. Vesuvius has an altitude of 3000 feet. A person stands 120 feet away from the base of the volcano. What is the angle of elevation from the person on the ground to the top of the volcano?

Answer: the angle of elevation from the person on the ground to the top of the volcano is 87.7°

Step-by-step explanation:

The person, his angle of elevation and his distance from the foot of the mountain forms a right angle triangle.

The altitude of the mountain represents the opposite side of the right angle triangle.

The distance of the person from the base of the volcano represents the opposite side of the right angle triangle.

To determine the angle of elevation from the person on the ground to the top of the volcano, we would apply the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan θ = 3000/120 = 25

θ = Tan^-1 (25)

θ = 87.7° to the nearest tenth.