The height of the top section of the tower is 32 feet.
The radio station tower is built in two sections. The tower is 87 feet from the viewing point. The angle of elevation of the bottom section is 25 degrees. The angle of elevation from the top of tower (both sections) is 40 degrees. Let the height of the bottom section be y and height of the bottom and top section be z.
Considering a right-angled triangle, tangent formula states that:
Tan ɵ = opposite side/ adjacent side where ɵ is the angle of elevation.
Hence, when ɵ = 25, opposite side = y, and adjacent side = 87
Tan 25 = y/ 87
y = 40.57 feet
Hence, when ɵ = 40, opposite side = z, and adjacent side = 87
Tan 40 = z/87
y = 73 feet
Let the height of the top section of the tower be x.
Hence, x = 73 - 40.57 = 32.4 ≈ 32 feet
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