Answer:
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
