Question

Suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is 60°. what is the length of the third side of the triangle?

Answer 1

To find the length of the third side of the triangle, the law of cosines is needed.

Let's say, for the sake of solving this problem the side with the length of 2 is a, that with the length of 5 is b, and the unknown is c.  The known angle here will be called C.

$c^2=a^2+b^2-2abcosC$

$c^2=2^2+5^2-(2*2*5*cos60) (cos60=0.5) c^2=4+25-(20*0.5) c^2=29-10 c^2=19 c= \sqrt{c^2} c= \sqrt{19}$

Answer 2

2^2+5^2=c^2
Radical 29 is the 3rd side