Question

Two ships leave a port at the same time. One goes 24km/h in the direction North 45 degree east and other travels 32km/h in the direction South 75 degree east. find the distance between the ships at the end of 3 hrs.

Answer 1

Hey there !

( Look at the above figure that is in attachment )

Solution :-
===========

⇒1st ship goes 24 kmph for 3 hours,

$OA = \frac{24km}{hour} * 3hour$

= 72 Km

So, the First ship travels 72 km.

⇒ 2nd ship goes 32 kmph for 3 hours

$OB = \frac{32km}{hour} * 3hour$

= 96 Km.

So, the Second ship travels 96 Km.

∴ ∠AOB = 45° + ( 90° + 75° )
= 60°

So, AB² = OA² + OB² - 2 × OA × OB × Cos60°

$= 72^{2} + 96^{2} - 2 * 72 * 96 * \frac{1}{2}$

$AB = \sqrt{ 72^{2}+ 96^{2} - 72* 96$

= 86. 53 Km . Ans