Question

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60° . If the tower is 30m high.
Find the length of building?

Answer 1

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60° . If the tower is 30m high.

Find the length of building?

Answer 2

Answer:

${ \huge{ \underline{ \sf{ \red{Solution:}}}}}$

⇒ Let the height of the tower (BC) = 30m

⇒ The height of the building (AD) = h m

⇒ Angle of elevation from the bottom of building to the top of tower and bottom of to the top of building are angle BAC = 60° ; ACD = 30°

Let AB = xm be the distance between foot of the tower and building

From, right angled ΔABD ,

${ \sf{Tan 30° = \frac{AD }{AB} }}$

$\to{ \sf{ \frac{1}{ \sqrt{3} } = \frac{h}{x} }}$

$\to{ \sf{h = \frac{x}{ \sqrt{3} }.....(1) }}$

From right angled ΔBAC,

${ \sf{Tan 60° = \frac{BC }{AB} }}$

$\to{ \sf{ \sqrt{3} = \frac{30}x{} }}$

$\to{ \sf{x = \frac{30}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{30 \sqrt{3} }{3} = 10 \sqrt{3} }}$

${ \boxed { \to \sf{x = 10 \sqrt{3} m}}}$

From 1 we get,

${ \sf{h = \frac{x}{ \sqrt{3} } }}$

${ \to{ \sf{h = \frac{10 \sqrt{3} }{ \sqrt{3} } = 10m}}}$

Therefore,

• Height of the building is 10m