Question

The Columbia Tower in Seattle is 954 feet tall. The Seafirst Tower is T feet tall and stands d feet away from the Columbia Tower. Find the height of the Seafirst Tower. Give your answer to 2 decimal places.

Answer 1

The specification of the problem includes a sketch of the relation between the towers showing two angles.

The sketch shows the segment of the track between the two towers (d), the heights of the two towers (954 feet and T),  and the horizontal angles from the base of each tower to the top of the other tower.

Then you can write two trigonometric ratios.

1) From the triangle formed by the segment that separates the two towers, d, and the height of Sears Tower (T) with horizontal angle 27°:

tan (27°) = T / d => d = T / tan(27°)

2) From the triangle formed by the segment that separates the two towers, d, and the height of Comumbia Tower (954), with horizontal angle 53°

tan(53°) = 954 / d = > d = 954 / tan(53°)

Now you can equal the two equations => 954 / tan(53) = T / tan(27) =>

T = 954 tan(27) / tan (53) =   366.29 feet

Answer: 366.29 feet