Chapter 8.6, Problem 10CE

To determine

To state: two different equations to get the value of x .

Answer to Problem 10CE

Two equations to get the value of x are $\cos 40°=\frac{x}{12}$ and $\sin 50°=\frac{x}{12}$ .

Explanation of Solution

Given:

The triangle is shown below:

  

Calculation:

In given triangle take cos of angle 40 degree as follows:

  $\begin{array}{c}\cos 40°=\frac{x}{12}\mathrm{......}\left(2\right)\\ \frac{x}{12}=0.766\\ x=9.192\end{array}$

In given triangle take sin of angle 50 degree as follows:

  $\begin{array}{c}\sin 50°=\frac{x}{12}\mathrm{......}\left(2\right)\\ \frac{x}{12}=0.766\\ x=9.192\end{array}$

Hence, two equations to get the value of x are $\cos 40°=\frac{x}{12}$ and $\sin 50°=\frac{x}{12}$ .