Question #135073
The bearing of a lighthouse from ship A is 29°NE and the bearing of that same lighthouse from ship B is 61°NW. If ship A and ship B are on the east-west line 200 km apart, how far is ship B from the lighthouse?
1
Expert's answer
2020-09-28T09:44:37-0400
SolutionSolution

The distance between ship B and the lighthouse can be obtained as below.The\ distance\ between\ ship\ B\ and\ the\ lighthouse\ can\ be\ obtained\ as\ below.\\

Let the distance be denoted by X which is the Adjacent side of the triangle.

Use the formula; SOH CAH TOA,SOH\ CAH\ TOA, \\

Cosθ=AdjecentHypotenuse    Cos 29 =Adjacent200    200 Cos 29=Adjacent Adjacent=174.92kmCos\theta=\frac{Adjecent}{Hypotenuse} \implies Cos\ 29^{\circ}\ = \frac{Adjacent}{200}\\ \implies200\ Cos\ 29^{\circ}=Adjacent\\ \therefore\ Adjacent=174.92km

Below is an image to show the triangle.


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