Two ships leave a port at the same time

Asked by admin @ in Math viewed by 319 People

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.

Answered by admin @


Hey there !

Look at this

( Firstly see the abvove figure that is in attachment );

Solution :-
========

⇒1st Ship goes 24Kmph for 3 hours ,

OA = \frac{24Km}{hr}* 3hr

= 72 km

So, The 1st ship travels 72 km


⇒2nd Ship goes 32Kmph for 3 hours,

OB = \frac{32Km}{hr}* 3hr

= 96 Km

So, The 2nd Ship travels 96Km

∴∠AOB = 45° + (90°+ 75°)
= 60°

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

= 72² + 96² - 2 × 72 × 96 × 1/2

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

= 86.53 Km (Ans).

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