A radio tower is located 275 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 37 and that the angle of depression to the bottom of the tower is 35 . How tall is the tower?

399.8 feet

Step-by-step explanation:

Since the angle of elevation of the top of the tower from the building is Ф = 37°, and the distance between the tower and the building is x = 275 feet. Let the upper part of the tower be h. These three components from a right-angled triangle with opposite side = h and adjacent side = x. So, by trigonometric ratios,

tanФ = h/x

h = xtanФ

= 275 feet × tan37°

= 275 feet × 0.7536

= 207.23 feet

Also, the angle of depression of the bottom of the tower from the building is Ф' = 35°, and the distance between the tower and the building is x = 275 feet. Let the lower part of the tower be h'. These three components from a right-angled triangle with opposite side = h' and adjacent side = x. So, by trigonometric ratios,

tanФ' = h'/x

h' = xtanФ'

= 275 feet × tan35°

= 275 feet × 0.7002

= 192.56 feet

So, the height of the tower, H = h + h'

= 207.23 feet + 192.56 feet

= 399.79 feet

≅ 399.8 feet

answer: 88

step-by-step explanation: