Chapter 6, Problem 7CR

To determine

To calculate:

Solve triangle by using law of sine.

Answer to Problem 7CR

There will be two values of triangle $\angle A=20°.4,\angle C=9°.6$

Explanation of Solution

Given information:

  $A=95°,a=51.2,b=33.7$

Calculation:

Apply sin rule to find other sides,

  $\frac{b}{\sin B}=\frac{c}{\sin C}$

Substitute all the values,

  $\begin{array}{l}\frac{30}{\sin 150°}=\frac{10}{\sin C}\\ \frac{30}{0.5}=\frac{10}{\sin C}\\ 60=\frac{10}{\sin C}\\ \sin C=\frac{1}{6}\\ c=9°.6\end{array}$

Sum of the here angles in a triangle is $180°$

  $\begin{array}{l}\angle A+\angle B+\angle C=180°\\ \angle A+150°+9°.6=180°\\ \angle A=180°-159°\\ \angle A=20.4°\end{array}$

Apply sin rule to find other coordinates,

  $\frac{a}{\sin A}=\frac{b}{\sin B}$

Substitute all the values,

  $\frac{a}{\sin 20°.4}=\frac{b}{\sin 150°}$

Multiply both sides by $\sin 20°.4$ ,

  $\begin{array}{l}a=\frac{30}{\sin 150°}\times \sin 20°.4\\ a=20.91\end{array}$

Hence, the other two sides are,

  $\angle A=20°.4,\angle C=9°.6$

Thus, there will be two values of triangle $\angle A=20°.4,\angle C=9°.6$