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
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)#