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 42° and that the angle of depression to the bottom of the tower is 37°. How tall is the tower?

Accepted Solution

Answer:The tower is approximately 381 feet high.Step-by-step explanation:Refer to the sketch attached. The height of the tower can be found in two parts:The part above the window, and The part under the window.Each part can be seen as a leg of a right triangle. The other leg is the distance between the building and the tower and is 300-feet long. The angle opposite to the leg is given. The length of the upper part is [tex]300\cdot \sin{42^{\circ}}[/tex] feet.The length of the lower part is [tex]300\cdot \sin{37^{\circ}}[/tex].The height of the tower is the sum of the two parts:[tex]300\cdot \sin{42^{\circ}} + 300\cdot \sin{37^{\circ}} = 300(\sin{42^{\circ}}+\sin{37^{\circ}}) = 381[/tex] feet.