Answer to Question #256283 in Trigonometry for Francis

Question

The bearing of a lighthouse from ship A is N29°E and the bearing of that lighthouse from ship B is N61°W. If ship A and ship B are on the east-west line 200 kilometers apart, how far is ship B from the lighthouse?

Answer 1

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

Use the formula; $SOH\ CAH\ TOA, \\$

$Cos\theta=\frac{Adjecent}{Hypotenuse} \implies Cos\ 29^{\circ}\ = \frac{Adjacent}{200}\\ \implies200\ Cos\ 29^{\circ}=Adjacent\\ \therefore\ Adjacent=174.92km$

Below is an image to show the triangle.