Chapter 12.1, Problem 32PPS

To determine

Calculate the value of $x^{\circ }$ .

Answer to Problem 32PPS

The value of $x^{\circ }$ is ${55.2}^{\circ }$ .

Explanation of Solution

Given:

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

  $\begin{array}{l}\cos \theta =\frac{p}{h}\\ \cos x^{\circ }=\frac{4}{7}\\ x^{\circ }={\cos }^{-1}(\frac{4}{7})\\ x^{\circ }={55.2}^{\circ }\end{array}$

Conclusion:

The value of $x^{\circ }$ is ${55.2}^{\circ }$ .