Question

Power point on the ground the angles of elevation on the bottom and top of a transmission tower fixed at the top of a 20 m high building a 45 degree and 60 degree respectively find the height of the tower

Answer 1

This may help you........

Answer 2

Let AB be the building of height 20m and BC be the tower of height h metres.

Let O be the point if observation.

Then,

$\sf{\angle{AOB}=45°,\angle{AOC}=60°}$

From right ∆OAB, we have

$\longrightarrow$$\sf{tan45°= \frac{AB}{OA} = 1 = \frac{20}{OA}}$

$\longrightarrow$$\sf{OA=20m}$

From right ∆OAC, we have,

$\longrightarrow$$\sf{tan60°= \frac{AC}{OA} = √3 = \frac{h+20}{20}}$

$\longrightarrow$$\sf{h=20(√3-1)m}$

Hence, the height of the tower is 20(√3-1)m.