Chapter 13.1, Problem 23PPS

To determine

Calculate the value of x .

Answer to Problem 23PPS

The value of x is $10.4$ .

Explanation of Solution

Given:

It is given in the question that the figure is given below in which b is given:

  

Concept Used:

In this, use the concept of pythagoras theorem and trigonometric ratios and the formula will be $h^2=p^2+b^2$ , $\sin \theta =\frac{p}{h},\cos \theta =\frac{b}{h},\tan \theta =\frac{p}{b},\csc \theta =\frac{h}{p},\sec \theta =\frac{h}{b},\cot \theta =\frac{b}{p}$ .

Calculation: Here, use the trigonometric ratios,

  $\begin{array}{l}\tan \theta =\frac{p}{b}\\ \tan {30}^{\circ }=\frac{x}{18}\\ \frac{1}{\sqrt{3}}=\frac{x}{18}\\ x=\frac{18}{\sqrt{3}}\\ x\approx 10.4\end{array}$

Conclusion:

The value of x is $10.4$ .