If you know the lengths of two sides, a and b, and the included angle, C, then
area = 0.5*a*b*sin(C)
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when trying to find the angle of a right triangle using only the opposite leg and the hypotenuse, eg. angle =sin opp leg over hyp * * * * * Also to find the area of a triangle if two sides and the included angle are known. Or the area of a sector of a circle.
Using the cosine and sine rules the area of the triangle works out as 457 square cm rounded.
By using the Sine rule: a/sinA = b/sinB = c/sinC
The sine of an angle in a right triangle is opposite/hypotenuse, where opposite is the only side that is not adjacent to the angle you want to find the sine of, and the hypotenuse is the side opposite the right angle in the triangle. Just find opposite/hypotenuse.
Sine ratio = opposite/hypotenuse