Chapter 6, Problem 3CR

To determine

To calculate:

Solve triangle by using law of sine.

Answer to Problem 3CR

There will be two values of triangle $b=9.11,a=2.54$

Explanation of Solution

Given information:

  $A=16°,B=98°,a=8.4$

Calculation:

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

  $\begin{array}{l}\angle A+\angle B+\angle C=180°\\ 16°+98°+\angle C=180°\\ 114°+\angle C=180°-114°\\ \angle C=180°-114°\\ \angle C=66°\end{array}$

Apply sin rule to find other coordinates,

  $\frac{b}{\sin B}=\frac{c}{\sin C}$

Substitute all the values,

  $\frac{b}{\sin 98°}=\frac{8.4}{\sin 66°}$

Multiply both sides by $\sin 98°$ ,

  $\begin{array}{l}b=\frac{8.4}{\sin 66°}\times \sin 98°\\ b=9.11\end{array}$

  $\frac{a}{\sin A}=\frac{b}{\sin B}$

Substitute all the values,

  $\frac{a}{\sin 16°}=\frac{b}{\sin 98°}$

Multiply both sides by $\sin 16°$ ,

  $\begin{array}{l}a=\frac{9.11}{\sin 98°}\times \sin 16°\\ a=2.5357\\ a=2.54\end{array}$

Hence, the other two sides are,

  $b=9.11,a=2.54$

Thus, there will be two values of triangle $b=9.11,a=2.54$