Question

A lighthouse is set 10 meters back from the edge of the shoreline, and it's beacon is 52 meters above sea level. Lucy can see the beacon from her ship, and the of elevation is 18 degrees. Her eyes are 12 meters above sea level. How far is the ship from the shoreline to the nearest meter?

Answer 1

The distance of the ship from the shoreline is 113 metres.

Explanation:

Please kindly check the attached files for explanation

Answer 2

The distance of the ship to the shoreline is 113 meters

Explanation:

Here we have the following information

Location of lighthouse = 10 m back from the edge of the shoreline

Height of beacon above sea level = 52 m

Level of the eyes of Lucy above sea level = 12 m

Angle of elevation of the beacon from Lucy = 18°

Therefore, the beacon, the elevation of the eyes of Lucy and the base of the lighthouse at the same elevation with Lucy form a right triangle with opposite side to angle = 52 m and angle = 18 °

Therefore, from

`Tan\theta =(sin\theta )/(cos\theta ) = (Opposite \, side \, to\, angle)/(Adjacent\, side \, to\, angle)`

We have

`Tan18 =(52-12)/(Adjacent ) = (40)/(Adjacent)`

0.325 =
`(40)/(Adjacent)`

Where the adjacent side is the distance of the ship from the lighthouse

Adjacent side = 40/0.325 = 123.107 meters

We recall that the lighthouse is 10 m back from the edge of the shoreline, therefore the ship is 123.107 - 10 or 113.107 meters from the shore line which is 113 meters to the nearest meter.