Chapter 13.1, Problem 28WE

To determine

To find: The all to three significant digits and angles.

Answer to Problem 28WE

The remaining angle is ${75}^o$ and remaining sides are $a\approx 23$ and $c\approx 23$ .

Explanation of Solution

Given information:

The given angle $\angle A={75}^o$ , $\angle B={30}^o$ , and side $b=12$ .

Calculation:

Consider the triangle.

  $\angle A={75}^o$ , $\angle B={30}^o$ , $b=12$ .

  $\begin{array}{l}C={180}^o-\left(75+30\right)\\ C=75\end{array}$

Now, use the law sine to find other two side.

  $\frac{a}{\sin A}=\frac{b}{\sin B}$

Substitute the value of $b,c$ , to get the $C$ .

  $\begin{array}{c}a=\sin {75}^o\left(\frac{b}{\sin B}\right)\\ \approx 23\end{array}$

Again,

  $\begin{array}{c}\frac{c}{\sin C}=\frac{b}{\sin B}\\ c=\sin {75}^o\left(\frac{12}{\sin 30}\right)\\ \approx 23\end{array}$

Therefore, the remaining angle is ${75}^o$ and remaining sides are $a\approx 23$ and $c\approx 23$ .