Question

In △ABC, m∠A=52°, c=11, and m∠B=19°. Find a to the nearest tenth.

Answer 1

From the problem we have

In △ABC, m∠A=52°, c=11, and m∠B=19°.

Draw the diagram with the help of given information, (see the attached image)

Now using Sine Law in the Triangle ABC, we can write

Now from Triangle ABC , we can write

$\frac{a}{sin52}=\frac{11}{sin109}$

Now simplify , we get

$\Rightarrow a=\frac{11}{sin109}*sin52\\ \\ \Rightarrow a=\frac{11}{0.9455}*0.7880\\ \\ \Rightarrow a=9.1676 \approx 9.2$