Question

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?

Answer 1

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 this

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)`