Question

A ship of height 9 meters is sighted from a lighthouse. From the top of the lighthouse, the angle of depression to the top of the mast and the base of the ship equal 30 degrees and 45 degrees respectively. How far is the ship from the lighthouse?

Answer 1

`21.276` meters

Explanation:

For the two angle of depressions one at the top of mast and other at the base will provide two distinct equation is terms of distance between the ship and lighthouse.

Let the distance between the ship and lighthouse be represented by X

y be the vertical distance above height of ship i.e
`9` meters.

Equation 1

`tan 45 = (Y + 9)/(X)`

or

`Y = X tan 45 - 9`

Second equation

`tan 30 = (Y)/(X) \\`

Or

`Y = X tan 30`

Equating both the equation 1 and 2 we get -

`X tan 30 = X tan 45 - 9\\X tan45 - X tan 30 = 9\\X * 1 - X * 0.577 = 9\\0.423 X = 9\\X = 21.276`