Question

The angle of depression of the top and bottom of the building which situated on one side of the road seen from the top of the tower situated on the other side of the road are respectively 45° and 60°. If height of the building is 10 m, find the height of the tower.​

Answer 1

Step-by-step explanation:

Let AB is a building of height 12m. CE is a tower. Let ED=h m.

The angles of depression from point E of top of tower at the roof and base on building are 45

0

and 60

0

respectively. Now

∠XEA=∠EAD=45

0

(Alternate angle)

∠XEB=∠EBC=60

0

(Alternate angle)

Let BC=x and ED=h m

AB=CD=12m

From right angled ΔEAD,

tan45°=

AD

ED

l=

x

h

h=x …(i)

From right angled ΔEBC,

tan60°=

BC

h+12

3

=

x

h+12

=

h

h+12

(Put the value of x from equation)

3

h=h+12

3

h–h=12

h[1.732–1]=12

h=

0.732

12

=16.393m

Hence, height of tower =EC=CD+ED

=12+16.393

=28.393m