Question

from the top of a cliff 50 m high, the angles of depression of the top and bottom a tower are observed to be 30° and 45° respectively. find the height of the tower

Answer 1

Answer:

HERE THE ANSWER

Step-by-step explanation:

So the height of the tower(AB) be h m

Next,the height of the cliff(PQ) = 50m

Angle of depression at A = 30°

Angle of depression at B= 45°

Let QB the distance between the tower and cliff be x

Now ,

From the angel PBQ we get

PQ/QB=50/x

so tan45°= 50/x=1

therefore,x=50

Now again,

From the angel PAT we get

tan30°=50-h/50

or,1/√3=50-h/50

or,50/√3=50-h

or,h=50-50/√3

or,h=(50√3-50)/√3

Now if value of √3 is given then put the value in place of √3 and you will get the value of h (the height of the tower)..... I hope this will help you.

Answer 2

Answer:

Step-by-step explanation:

HERE THE ANSWER

Step-by-step explanation:

So the height of the tower(AB) be h m

Next,the height of the cliff(PQ) = 50m

Angle of depression at A = 30°

Angle of depression at B= 45°

Let QB the distance between the tower and cliff be x

Now ,

From the angel PBQ we get

PQ/QB=50/x

so tan45°= 50/x=1

therefore,x=50

Now again,

From the angel PAT we get

tan30°=50-h/50

or,1/√3=50-h/50

or,50/√3=50-h

or,h=50-50/√3

or,h=(50√3-50)/√3