Question

The angle of elevation of the top of a building from the foot of a 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 50 m high, find the height of the building​

Answer 1

Answer:

Given height of tower CD=50m

Let the height of the building, AB=h

In right angled △BDC,

⇒  tan60o=BDCD

⇒  3=BD50

⇒  BD=350m

In right angled △ABD,

⇒  tan30o=BDAB

⇒  31=350h

∴  31=503h

∴  h=350=16.66m

∴  The height of the building is 16.66m.

Answer 2

Step-by-step explanation:

Answer:

Given height of tower CD=50m

Let the height of the building, AB=h

In right angled △BDC,

⇒  tan60o=BDCD

⇒  3=BD50

⇒  BD=350m

In right angled △ABD,

⇒  tan30o=BDAB

⇒  31=350h

∴  31=503h

∴  h=350=16.66m

∴  The height of the building is 16.66m.