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From her window, Neta looks up to the top of a neighboring building at an angle of 56°. Her angle of depression to the bottom of the building is 32°.

The neighboring building is 150 feet away from the building Neta is in.

How tall is the neighboring building?

Enter your answer, rounded to the nearest tenth of a foot, in the box.

The building is 316.1 feet tall

Step-by-step explanation: Please refer to the attached diagram for details.

Based on the information provided, Neta is at point W, and looks at the top of a building from an angle of elevation measuring 56 degrees and then looks down to the bottom of the building at an angle of depression measuring 32 degrees. The top of the building is point T while the bottom is point B. A line separating angles 56 and 32 is drawn to point M along the line TB. So we now have two right angled triangles, WTM and WBM. In effect, the length of the building which is line TB has been divided into lines x and y.

From triangle WTM, using angle 56 as the reference angle, we calculate x as;

TanW = opposite/adjacent

Tan56 = x/150

By cross multiplication we now have

Tan56 (150) = x

1.4825 (150) = x

x = 222.375

Also, from triangle WBM, using angle 32 as the reference angle, we calculate y as,

TanW = opposite/adjacent

Tan32 = y/150

By cross multiplication we now have

Tan32 (150) = y

0.6249 (150) = y

y = 93.735

Therefore the entire length of the building can be derived from x + y

Length = x + y

Length = 222.375 + 93.735

Length = 316.11

To the nearest tenth of a foot, the building is 316.1 feet tall.