Question

a tugboat is 36km due north of lighthouse C. Lighthouse B is directly east of lighthouse C. The lighthouses are 53km apart. Find the bearing og lighthouse B from the tugboat and the distance of lighthouse B from the tugboat.

Answer 1

The figure of this problem is

From this figure,

$tan\alpha = \dfrac{53}{36}$

$\alpha = tan^{-1}(\dfrac{53}{36})$

$\alpha = 55.81 ^ \circ$

Now, we can use Pythagorean Theorem

$d = \sqrt{53^2+36^2}$

$d = 64.07 km$