Question

Two boats,70 metres apart and on opposite sides of a light-house,are in a straight line with the light house.The angles of elevation of the top of the light house from the two boats are 71.6o and 45o,find the height of the light-house(tan71.6o=3).

Answer 1

Let AB be the light house with height h metres.

Two boats are at C and D and are 70 metres apart.

(As shown in the Figure)

$\rule{200}{2}$

In right angled triangle ABC :-

$tan \theta=\dfrac{h}{CB}\\ \\ \\ \dfrac{h}{CB}=3\\ \\ \\h=3CB$

Again,

In right angled triangle ABD :-

$tan \theta=\dfrac{h}{BD}\\ \\ \\ \dfrac{h}{BD}=1\\ \\ \\h=BD$

$\rule{200}{2}$

From above two equations :-

H= 3CB

H=BD

$3CB=BD\\ \\ \\3(CD-BD)=BD\\ \\ \\3CD-3BD=BD\\ \\ \\4BD=210\\ \\ \\BD=\dfrac{210}{4}\\ \\ \\BD=52.5\:m$

$\rule{200}{2}$

We already know that

H=BD

Thus,

Height of the Light house is equal to 52.5 metres.

$\rule{200}{2}$

Answer 2

Answer :-

Height of the Light house is equal to 52.5 metres.

Solution :-

Refer to the Attachment.

Hope it Helps !!!!