A building 200 feet tall casts a 80 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the

Question

3 years ago

9

A building 200 feet tall casts a 80 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the

building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (assume the person's eyes are 4 feet above ground level.)

Mathematics

1 answer:

mr Goodwill [35] · Answer 1 · 2022-04-04T18:15:03+03:00

Answer: 67.80°

Step-by-step explanation:

A right angle triangle is formed. The height of the building represents the opposite side of the right angle triangle. The length of the shadow represents the adjacent side of the right angle triangle.

Since the person's eyes are 4 feet above ground level, the opposite side of the triangle would be

200 - 4 = 196 feet

To determine the angle of the person's eyes, θ to the top of the building, we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan θ = 196/ 80 = 2.45

θ = Tan^-1(2.45)

θ = 67.80°