Question

Solve a triangle when A=15° B=113° and b=7?

Answer 1

Let us draw a triangle ABC with A=15° ,B=113° and b=7.

Please see the attached image.

We know that the sum of interior angles of a triangle is 180 degrees. Thus, we have

`A+B+C=180\\ \\ 15+113+C= 180\\ \\ C=62^(\circ)`

Apply Sine rule in the triangle ABC, we get

`(a)/(\sin 15)= (7)/(\sin 113)\\ \\ a=(7 \sin 15)/(\sin 113)\\ \\ a=1.97\\ \\ \text{Again apply sine rule, we get}\\ \\ (c)/(\sin 62)= (7)/(\sin 113)\\ \\ c=(7 \sin 62)/(\sin 113)\\ \\ c=6.71`

Therefore, we have

`a=1.97\\ c=6.71\\ C=62^(\circ)`