Question

The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10m. longer than when it was 60°, Find the height of the tower.
​plz answer me fast....its urgent......

Answer 1

Let AB be the tower and let AC and AD be its shadows when the angles of elevation of the sum are 60

o

and 45

o

, respectively. Then,

∠ACB=60

o

,∠ADB=45

o

,CD=10 m

Let AB=h metres and AC=x metres

In right △CAB, we have,

tan60

o

=

AC

AB

3

=

x

h

x=

3

h

......(1)

In right △ DAB, we have,

tan45

o

=

AD

AB

1=

10+x

h

x=h−10 .....(2)

From 1 and 2, we get,

3

h

=h−10

h=

3

h−10

3

3

h−h=10

3

h(

3

−1)=10

3

h=5

3

(

3

+1)

h=15+5

3

m