Question

An observer on the top of a cliff 200m above the sea level the angles of depression of two ships at anchor to be 45 degree and 60 degree respectively find the distance between the two ships of the line joining the points to the base of the cliff

Answer 1

The distance between the two ships is 84.52 meters.

Step-by-step explanation:

Given that,

Height of the cliff, h = 200 m

The angles of depression of two ships at anchor to be 45 degree and 60 degree respectively.

We need to find the distance between the two ships of the line joining the points to the base of the cliff.

The attached figure shows the whole scenario. It is given that,

$tan(45)=\dfrac{200}{x+y}$

$x+y=200$............(1)

Similarly,

$tan(60)=\dfrac{200}{x}$

$\sqrt3=\dfrac{200}{x}$

$x=\dfrac{200}{\sqrt3}$

Put the value of x in equation (1) we get :

y = 84.52 meters

So, the distance between the two ships is 84.52 meters. Hence, this is the required solution.

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