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

Here is the sketch of the case above

Let the distance from the lighthouse to ship B be x.

Clearly from the figure above, a right-angle triangle if formed.

For us to find the value of x, we apply the trigonometric ratios of SOHCAHTOA, whereas we use the sine ratio;

$sin (61°) = \frac{Opposite}{Hypotenuse}$

$sin (61°) = \frac{x}{200}$

$x = 200 sin (61°)$

$= 174.92$

$x= 174.92 km$

Therefore, the distance from ship B to the lighthouse is $174.92 km$