Chapter 8, Problem 15CT

To determine

To find: the value of x

Answer to Problem 15CT

The value of x is $x=14$

Explanation of Solution

Given Information: A right angled triangle with acute angle 30⁰ and adjacent side of measure

  $7\sqrt{3}$

Formula used:

In a right triangle the cosine of the angle is the ratio of the measure of side adjacent to the angle to the hypotenuse.

  

It can be expressed as,

  $\cos B=\frac{b}{c}$

Calculation: Consider the right triangle given below.

  

Here, considering the triangle,

  $\begin{array}{c}\cos 30°=\frac{7\sqrt{3}}{x}\\ x=\frac{7\sqrt{3}}{\cos 30°}\\ =\frac{7\sqrt{3}}{\sqrt{3}/2}\\ =14\end{array}$ .