Question

Please help me!

The angle of elevation of the top of a tower to a point on the ground is 61°. At a point 600 feet farther from the base, in line with the base and the first point and in the same plane, the angle of elevation is 32°. Find the height of the tower.

Answer 1

574

Explanation:

Answer 2

573.6 ft

Explanation:

The mnemonic SOH CAH TOA reminds you of the relationship of right triangle sides and angles:

Tan = Opposite/Adjacent

This tells us ...

tan(61°) = (height)/(distance to first point)

or

distance to first point = height/tan(61°)

Likewise, ...

distance to second point = height/tan(32°)

Then the difference of the distances is ...

distance to second point - distance to first point

= height/tan(32°) -height/tan(61°)

600 ft = height × (1/tan(32°) -1/tan(61°))

Dividing by the coefficient of height, we have ...

height = (600 ft)/(1/tan(32°) -1/tan(61°)) ≈ (600 ft)/(1.04603) ≈ 573.6 ft