A triangle has sides of lengths 6 and 9 and unknown included

A triangle has sides of lengths 6 and 9 and unknown included angle . If the area of the triangle is 13.5, find the angle . Give your answer in radians. If there is more than one possible answer, give them as a comma separated list.

Solution

(1/2 ab)sin = area
.5*6*9 sin =13.5
27 sin =13.5
dividing both sides by 27
(27 sin )/27=13.5/27
sin =0.5=1/2
so, =pi/6,5pi/6