Question

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is `(13pi)/24` and the angle between B and C is `(pi)/24`. What is the area of the triangle?

Answer 1

Area of triangle is `1.449` units.

Explanation:

The formula for area of a triangle given two sides `a` and `b` and included angle `theta` is `1/2xxabxxsintheta`.

Here, though we have been given two sides as `1` and `3`, included angle has not been given.

But as other two angles are `(13pi)/24` and `pi/24`, third angle will be given by

`pi-(13pi)/24-pi/24=(24pi-13pi-pi)/24=(10pi)/24`

Hence area of triangle is `1/2xx1xx3xxsin((10pi)/24)`

= `3/2xx0.9659=1.449` units.