Chapter 12.1, Problem 37PPS

To determine

Calculate the value of x and y.

Answer to Problem 37PPS

The value of x and y are $21.9$ and $20.8$ .

Explanation of Solution

Given:

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

  

Concept Used:

In this, use the concept of pythgoras 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,

For x,

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {46.5}^{\circ }=\frac{x}{30.2}\\ 0.725=\frac{x}{30.2}\\ x=0.725\cdot 30.2\\ x\approx 21.9\end{array}$

Again for y,

  $\begin{array}{l}\cos \theta =\frac{b}{h}\\ \cos {46.5}^{\circ }=\frac{y}{30.2}\\ 0.688=\frac{y}{30.2}\\ y=30.2\cdot 0.688\\ y\approx 20.8\end{array}$

Conclusion:

The value of x and y are $21.9$ and $20.8$ .