Chapter 12.1, Problem 36PPS

To determine

Calculate the change in altitude of the hang glider .

Answer to Problem 36PPS

The value of altitude x is $21.8$ feet.

Explanation of Solution

Given: It is given in the question that the horizontal distance of $60feet$ and at an angle of ${20}^{\circ }$ .

  

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:

Let x be the length of the altitide. In this, an angle, an adjacent side are given.

Here, use the trigonometric ratios,

  $\begin{array}{l}\tan \theta =\frac{p}{b}\\ \tan {20}^{\circ }=\frac{x}{60}\\ 0.363=\frac{x}{60}\\ x=60\cdot 0.363\\ x\approx 21.8\end{array}$

Conclusion:

The value of x is $21.8$ feet.