A tower is a tall structure, taller than it is wide, often by a significant margin. Towers are distinguished from masts by their lack of guy-wires and are therefore, along with tall apartment buildings, self-supporting structures. Towers are specifically distinguished from "apartment buildings" in that they are not built to be habitable but to serve other functions. Karan went to city and he saw a transmission tower fixed at the top of a high building. He come to know that the height of the building is 20m. From a point on the ground, the angles of elevation of the top and the bottom of a transmission tower are and respectively such that cos = sin(1500 – ) and sin2 = cos(1350 – 3). Find the height of the tower.
Answers
the height of the transmission tower = 14.64 m
Step-by-step explanation:
Cosα = Sin(150° - α)
=> Sin(90° - α) = Sin(180° - (150° - α))
=> 90° - α = α - 30°
=> 2α = 120°
=> α = 60°
Sin2β = Cos(135° - 3β)
=> Cos(90° - 2β) = Cos(135° - 3β)
=> 90° - 2β = 135° - 3β
=> β = 45°
height of the transmission tower. = h
Distance of building = d
Height of building = 20 m
Tanβ = Height of building/Distance of building
=> Tan 45° = 20/d
=> 1 = 20/d
=> d = 20
Tanα = (Height of building + Tower height)/Distance of building
=> Tan 60° = (20 + h) /d
=> √3 = (20 + h)/20
=> 20 + h = 20√3
=> h = 20√3 - 20
=> h = 20(√3 - 1) = 14.64 m
the height of the transmission tower = 14.64 m
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