Chapter 13, Problem 7STP

To determine

To find:value of $m$ .

Answer to Problem 7STP

Value of $m=7.4$ cm

Explanation of Solution

Given information:

  $\begin{array}{l}M={35}^0\\ n=12.4cm\\ N={74}^0\end{array}$

Concept:

Law of sines

  $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Given

  $\begin{array}{l}M={35}^0\\ n=12.4cm\\ N={74}^0\end{array}$

Using law of sines

We get

  $\begin{array}{l}\frac{\sin M}{m}=\frac{\sin N}{n}\\ \Rightarrow \frac{\sin {35}^0}{m}=\frac{\sin {74}^0}{12.4}\\ \Rightarrow m=\frac{12.4\sin {35}^0}{\sin {74}^0}\\ \Rightarrow m=\frac{12.4\left(0.574\right)}{0.9613}\\ \Rightarrow m=\frac{7.1176}{0.9613}\\ \Rightarrow m=7.4\end{array}$

Therefore,

Value of $m=7.4$ cm