Question

100 of the tower from this point,
1. The angle of elevation of the top of a towek from two points at a distance of 4 mand
Om from the base of the tower and in the same straight line with it are complementary
Prove that the height of the tower is 6 m​

Answer 1

Answer:

Given,

the angle of elevation of the top of the tower from two points P & Q is at a distance of a & b.

Also given, to prove that the tower

height=ab

(∵ complementary angle =(90o−θ))

From ΔABP

tanθ=BPAB=aAB ……..(1)

From ΔABQ

tan(90−θ)=BQAB

(∵tan(90−θ)=cotθ)

(cotθ=tanθ1)

We get,

cotθ=ABBQ=ABb ……..(2)

by equation (1) & (2) we get,

aAB=ABb

⇒AB2=ab⇔AB=ab

∴AB=height=ab

Hence proved.