Question

The angle of elevation of a cloud from a point 150m above the lake is 45°and the angle of depression of the cloud's reflection on the lake is 60°. Fine the height of the cloud.

Answer 1

Let A be the position of the cloud and B be the reflection of the cloud in lake.

Let E be the points xmetres above the lake making angle of angle of elevation θ with A and angle of depression 45

∘

with B

Let h be the height of the cloud

Now, from the figure

EF=DC=x

AC=BC=h

AD=h−x

BD=h+x

In ΔAED

tanθ=

ED

AD

=

ED

h−x

------- (1)

In ΔEDB

tan45

∘

=

ED

BD

ED=h+x ----- (2)

From (1) and (2)

tanθ=

h+x

h−x

h(tanθ−1)=−x(tanθ+1)

h=

1−tanθ

x(1+tanθ)

h=

1−tan45

∘

tanθ

x(tan45

∘

+tanθ)

(1=tan45

∘

)

=xtan(45

∘

+θ)

Thus the height of the cloud is xtan(45

∘

+θ