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.

Accepted Solution

Answer:   573.6 ftStep-by-step explanation:The mnemonic SOH CAH TOA reminds you of the relationship of right triangle sides and angles:   Tan = Opposite/AdjacentThis 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