Chapter 12.1, Problem 22PPS

To determine

Calculate the value of x .

Answer to Problem 22PPS

The value of x is $3.6$ .

Explanation of Solution

Given:

It is given in the question that the figure is given below in which h 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,

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {64}^{\circ }=\frac{x}{4}\\ \sin {64}^{\circ }=\frac{x}{4}\\ x=0.925\cdot 4\\ x\approx 3.6\end{array}$

Conclusion:

The value of x is $3.6$ .