# A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (7pi)/24#. What is the area of the triangle?

##### 1 Answer

By use of 3 laws:

- Sum of angles
- Law of cosines
- Heron's formula

The area is 3.75

#### Explanation:

The law of cosines for side C states:

or

where 'c' is the angle between sides A and B. This can be found by knowing that the sum of degrees of all angles is equal to 180 or, in this case speaking in rads, π:

Now that the angle c is known, side C can be calculated:

Heron's formula calculates the area of any triangle given the 3 sides by calculating half of the perimeter:

and using the formula: