Answer to Question #135073 in Trigonometry for Jefferson Broncate

Question

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?

Answer 1

$$Solution$$

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

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

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

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

Below is an image to show the triangle.