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

$\frac{a}{\sin 15}= \frac{7}{\sin 113}\\ \\ a=\frac{7 \sin 15}{\sin 113}\\ \\ a=1.97\\ \\ \text{Again apply sine rule, we get}\\ \\ \frac{c}{\sin 62}= \frac{7}{\sin 113}\\ \\ c=\frac{7 \sin 62}{\sin 113}\\ \\ c=6.71$

Therefore, we have

$a=1.97\\ c=6.71\\ C=62^{\circ}$