Question

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.)

Answer 1

The angle of a person's eyes to the top of a 200-foot building, standing at the end of an 80-foot shadow with eyes 4 feet above ground level, is approximately 67.98 degrees.

Step-by-step explanation:

To find the angle of a person's eyes to the top of a 200-foot building when standing at the end of an 80-foot shadow, with their eye height being 4 feet above the ground, we can use trigonometric functions, specifically the tangent function, which relates the angle θ to the opposite side over the adjacent side in a right-angled triangle. The building and its shadow, along with the viewer's eye line, form a right-angled triangle.

First, we adjust the building's height to account for the viewer's eye level:

• Building's actual height = 200 feet
• Viewer's eye level = 4 feet
• Adjusted building height = Building's actual height - Viewer's eye level = 196 feet

Now, we apply the tangent function:

• θ = tan⁻¹(opposite/adjacent)
• θ = tan⁻¹(196 feet / 80 feet)
• θ = tan⁻¹(2.45)

Using a calculator, we find that θ is approximately:

• θ ≈ 67.98°

Therefore, the angle of the person's eyes to the top of the building is approximately 67.98 degrees to the nearest hundredth of a degree.

Answer 2

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°