Question 1173231
Two boats leave a harbour at the same time and head out at an angle of 35o to each other. 
Boat A is travelling at 45 km/h and boat B is travelling at 52 km/h. 
How far apart are the two boats after two hours?
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            The problem is to find the third side of a triangle,  given its two sides and the angle between them.


            It is based on using the cosine law.  The Pythagorean formula,  used by @ewatrrr,  is  IRRELEVANT.



<pre>
One  side of the triangle is the traveled distance by boat A: it is  a = 45*2 = 90 km.


Over side of the triangle is the traveled distance by boat B: it is  b = 52*2 = 104 km.


The third side, according to the cosine law, is



    d = {{{sqrt(a^2 + b^2 - 2*a*b*cos(35^o))}}} = {{{sqrt(90^2 + 104^2 - 2*90*102*0.81933)}}} = 62.234 km.



<U>ANSWER</U>.  In two hours, the boats are  62.234 km apart.
</pre>

Solved.


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Do not accept any different answer.


Ignore the post by &nbsp;@ewatrrr, &nbsp;since her solution is &nbsp;INCORRECT.