Chapter 9.7, Problem 43E

To determine

To find: Value of x from right angle triangle.

Answer to Problem 43E

The value of $x=\frac{14}{\sqrt{3}}$ .

Explanation of Solution

Given information:

  

Formula used:

  $\cos \theta =\frac{Base}{Hypotenuse}$

  

Recall, $\cos \theta =\frac{Base}{Hypotenuse}$ ,

  $\begin{array}{l}\theta =30°\\ Base=7\\ Hypotenuse=x\end{array}$

  $\begin{array}{l}\cos 30°=\frac{7}{x}\\ \\ \frac{\sqrt{3}}{2}=\frac{7}{x}\\ \\ x=\frac{7\cdot 2}{\sqrt{3}}\\ \\ x=\frac{14}{\sqrt{3}}\end{array}$

The value of $x=\frac{14}{\sqrt{3}}$ .