Question

From the top of lighthouse AB The angel of depression of the top and bottom of building CD are 45° and 60° respectively If the building is 12 mts in height find out the height of the lighthouse and also the distance between the foot of the lighthouse and foot of the building (root3 = 1.73)

Answer 1

do like this just replace the value

Answer 2

Let A be the top of the lighthouse.

The angle of depressions are 45° and 60° to the top and bottom of the building.

Therefore,

EC=BD

Now,

In triangleAEC,

tan 45°=h\EC

EC=h

In triangleABD,

tan 60°=12+h/BD

√3=12+h/BD

BD√3=12+h

BD√3=12+EC

BD√3=12+BD

BD√3-BD=12

BD×0.73=12

BD=6.43m

Hence, the foot of the lighthouse

and the foot of the building

is 6.43m.