Given that B = arcsin(24/25), C = arcsin(12/13), and a = 17, find the area of triangle ABC.
Draw altitude AP with P on BC.
Since B = arcsin(24/25), sides AP and AB ( of triangle(APB) ) must be in the ratio 24/25.
Since C = arcsin(12/13), it is also true that C = arcsin(24/26) and that sides AP and AC
( of triangle(APB) ) must be in the ratio 24/26.
In triangle(APB), if AP = 24 and AB = 25, then BP = 7 (Pythagorean Theorem).
In triangle(APC), if AP = 24 and AC = 26, then CP = 10.
Since BP + CP = BC and since 7 + 10 = 17, BP must equal 10 and CP must equal 7.
The area of triangle(ABC) = ½·base·height = ½·BC·PA = ½·17·24 = .........