Can you help me find the height of building B?

Question

The distance between 2 buildings is 50 feet. The angle of elevation to the top of building B is 18 degrees. The angle of depression to the bottom of building B is 40 degrees. If possible can you round to the nearest tenth?

Answer 1

I assume the measurements are from the top of building A. Draw a picture and note that the height h₁ from the top of building A to the top of building B satisfies

h₁ / 50 = tan18°

Similarly, the height h₂ from the bottom of building B to the top of building A satisfies

h₂ / 50 = tan40°

So the height of building B is

h₁ + h₂ = 50 tan18° + 50 tan40° = 50(tan18° + tan40°) = ? feet