A radio tower...

Question

A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 25∘ and that the angle of depression to the bottom of the tower is 20∘. How tall is the tower?

Answer 1

So we are working with two different triangles in the problem. Picture two right triangles stacked on top of each other, one right side up and the other upside down. The edge they share is horizontal, and we can define it as the distance from the person to the tower (300ft). If we remember, tan(θ) is equal to the opposite side over the adjacent side where θ is the angle we are looking at. Using the distance to the tower we know the adjacent side, and the angles to the top and bottom so we can make our equations tan(25)*300 to get the height from the person to the top and tan(20)*300 to get the distance to the bottom. If we add them together you get the answer. I hope that helps!