A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is (pi)/8. What is the area of the triangle?

1 Answer
bp
Dec 16, 2015

22.96 (approx) sq units

Explanation:

Sides are marked with small letters. So the sides are a,b,c. Triangle is ABC. Side opposite A is a, side opposite B is b...... The triangle is like thisenter image source here

The area of the triangle would be 1/2 ab sinC

=1/2 120 sin (pi/8) = 60(0.3826)=22.96 (approx).

For exact value write cos(pi/4)= 1-2sin^2 (pi/8), that is

1/sqrt2 =1-2sin^2 (pi/8). Simplify for sin(pi/8) and plug in the Area expression 60 sin (pi/8)

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