Question

A man standing on the roof of a building 58.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.8°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.3°. How tall is the building next door? (Round your answer to the nearest tenth.)

Answer 1

check the picture below.

make sure your calculator is in Degree mode, since the angles are in degrees.

so "x" is about 25.15 or so, that simply means, the building are about 25 feet apart from each other.

notice, the smaller building is 50 - y in height.

and just a quick note, angle of depression means, the angle below the horizontal, or the angle going downwards from orientation.

Answer 2

The next door building is 37.8 feet tall.

Explanation:

Height of the building at which man is standing = AE = 58.0 feet

Height of the neighboring building = CD = x

Let AB = y

x+ y = 58 ft..[1]

In triangle ABC:

`\tan 34.8^o=(AB)/(BC)`

`0.6950=(y)/(BC)`...[2] (
`\tan 34.8^o=0.6950`)

In triangle AED:

`\tan 63.3^o=(AE)/(ED)`

`1.9883=(58.0 ft)/(ED)` (
`\tan 63.3^o=1.9883`)

`ED=(58.0 ft)/(1.9883)=29.1710 ft`

BC = ED

Putting value of ED in [2]

`0.6950=(y)/(115.3202 ft)`

`y=29.1701 ft* 0.6950=20.2743 ft`

Puttig value in y in [1], we get:

x = 58.0 ft - 20.2743 ft = 37.7257 ft ≈ 37.8 ft

The next door building is 37.8 feet tall.