# A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 8, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

##### 1 Answer

Feb 5, 2016

#### Explanation:

Let

Thus, you have:

#A = 10# ,#B = 8# ,#beta= (11 pi)/24# and#alpha = (3 pi)/8# .

Let's find out the length of the third angle first.

As the sum of all three angles in the triangle must be

#gamma = pi - alpha - beta = pi - (11 pi)/24 - (3 pi)/8 = pi/6#

Now you have the sides

#"Area" = 1/2 A * B * sin gamma#

#= 1/2 * 10 * 8 * sin(pi/6)#

#= 5 * 8 * 1/2#

#= 20 " units"^2#