Question:
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45 degree and 60 degree respectively. Find the height of the tower.
Answer:
Let BC is the height of building and CD is the height of the tower.
Given height of building = 20m
So BC = 20
Now From Δ ABC,
tan 45° = BC/AB
=> 1 = 20/AB
=> AB = 20
Again from Δ ABD,
tan 60° = BD/AB
=> √3 = (BC + CD)/AB (BD = BC + CD and tan 60° =√3 )
=> √3 = (20 + CD)/20
=> 20√3 = 20 + CD
=> CD = 20√3 - 20
=> CD = 20(√3 - 1)
So height of tower is 20(√3 - 1) m
Not what you are looking for? Go ahead and submit the question, we will get back to you.
