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.
