SOLUTION: The area of triangle PQR is 18. If p = 6 and q = 8, find all possible measures of angle R. Round your answers to the nearest tenth. Show the equation used.

For each triangle, its area is half of the product of the lengths of any its two sides and the sine of the angle between them.


In particular, for your triangle PQR


    its area = ,   or


    18 = ,

    18 = 24*sin(R).


It gives


    sin(R) =  =  = 0.75.


Therefore, R may have two and only two values


    1)  R = arcsin(0.75)             (acute angle),   and

    2)  R = 180° - arcsin(0.75)      (obtuse angle)