Question

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 7, 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?

Answer 1

The triangle does not exist

Explanation:

From the given data:

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 7, respectively. The angle between A and C is 13π/24 and the angle between B and C is 7π/24. What is the area of the triangle?

sides `a=2` and `b=7` and angle `B=(13pi)/24` and angle `A=(7pi)/24`

By the Sine Law

`a/(sin A)=b/sin B`

But

`2/sin ((7pi)/24)` not equal to `7/sin((13pi)/24)`

The triangle does not exist.

God bless...I hope the explanation is useful.