Precalculus angle elevation question

Question

A water tower is located x = 275 ft from a building (see the figure). From a window in the building, an observer notes that the angle of elevation to the top of the tower is 39° and that the angle of depression to the bottom of the tower is 25°.

How tall is the tower? (Round your answer to the nearest foot.)

How high is the window? (Round answer to the nearest foot.)

Answer 1

tan x = opposite/adjacent

The adjacent side is 275. For each angle, the opposite side is its portion of the height of the tower. Add them together.

275*tan39 degrees + 275*tan25 degrees = about 351 feet

From the figure, note that the height of the window is the lower portion of the height of the tower (the window is that height above the ground) = 275*tan25 degrees = about 128 feet