Question

35. a A pole of height h is at some distance from a tower. The angle of elevation of top of the tower from foot of the pole is θ and the angle of elevation of the top of the tower from the of the pole is Φ. Find the height of the top tower and its distance from the pole.​

Answer 1

Answer:

Let PQ be the tower and OA be the pole.

In △OPQ we have,

tanα=

OP

PQ

=

x

PQ

⇒PQ=xtanα ....(1)

⇒h+QR=xtanα

⇒QR=xtanα−h ....(2)

Step-2: For triangle ARQ.

We have,

tan(α−β)=

x

QR

⇒tan(α−β)=

x

xtanα−h

[using equation (2)]

⇒tan(α−β)=tanα−

x

h

⇒

x

h

=tanα−tan(α−β)

⇒x=

tanα−tan(α−β)

h

Therefore equation (1) become,

⇒ PQ=xtanα

=

tanα−tan(α−β

htanα

=

sinαcos(α−β)

sinαcos(α−β)−sin(α−β)

h×

cosα

sinα

=

sinβ/

hsinαcos(α−β)

Hence,The height of the tower is

sinβ/

hsinαcos(α−β)