Question

A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 2, respectively. The angle between A and C is `(5pi)/24` and the angle between B and C is `(pi)/24`. What is the area of the triangle?

Answer 1

`3.5355`

Explanation:

The angle between A and C is `(5pi)/24` and the angle between B and C is `pi/24`, Hence, angle between A and B is `pi-(5pi)/24-pi/24=(24-5-1)pi/24=(18pi)/24=(3pi)/4`

As sides A and B have lengths of `5` and `2` angle between them is `(3pi)/4`,

Area of the triangle is given by the formula `1/2bcsinA`

and hence it is `1/2xx5xx2xxsin(3pi)/4`

= `1/cancel(2)xx5xxcancel(2)xxsqrt2/2`

= `5xx1.4142/2=5xx0.7071=3.5355`