Question

A ship sets out to sail to a point 111 km due north. An unexpected storm blows the ship to a point 113 km due east of its starting point. (a) How far and (b) in what direction (as an angle from due east, where north of east is a positive angle) must it now sail to reach its original destination

Answer 1

Answer:

Ship has to  travel 158.4 km in the direction of $\theta =$ 44.48 ° N of W to reach its original destination.

Explanation:

From the ΔABC

AB = 111 KM

BC = 113 KM

Now from the pythagoras theorm

$AC^{2} = AB^{2} + BC^{2}$

$AC^{2} = 111^{2} + 113^{2}$

AC = 158.4 km

$\tan \theta = \frac{AB}{BC}$

$\tan\theta = \frac{111}{113}$

$\tan\theta$ = 0.9823

$\theta =$ 44.48 ° N of W.

Therefore ship has to  travel 158.4 km in the direction of $\theta =$ 44.48 ° N of W to reach its original destination.