Chapter 11.4, Problem 25E

To determine

To find the value of $\text{x}$ to the nearest tenth.

Answer to Problem 25E

The value of $\text{x}$ to the nearest tenth is $\text{x}=26.4$

Explanation of Solution

Given information:

The following figure is given:

  

Formula used:

The following formula for the definition of sine ratio is used:

  $\text{sinθ}=\frac{\text{perpendicular}}{\text{hypotenuse}}$

Calculation:

The value of $\text{x}$ to the nearest tenth can be calculated by:

  $\begin{array}{l}\sin {27}^{\circ }=\frac{12}{\text{x}}\left[\text{Definition of sine ratio}\right]\\ 0.454=\frac{12}{\text{x}}\left[\sin {27}^{\circ }=0.454\right]\\ 0.454\text{x}=12\left[\text{multiplying both sides by x}\right]\\ \frac{0.454\text{x}}{0.454}=\frac{12}{0.454}\left[\text{divide both sides by 0}\text{.454}\right]\\ \text{x}=26.431\left[\text{Round off to the nearest tenth}\right]\\ \text{x}=26.4\end{array}$

Hence, the value of $\text{x}$ to the nearest tenth is $\text{x}=26.4$