Chapter 12.9, Problem 30PPS

To determine

To calculate: the value of angle to the nearest tenth and to write the corresponding inverse trigonometric function.

Answer to Problem 30PPS

  $\theta ={\tan }^{-1}\left(\frac{59}{190}\right),{17.2}^{\circ }$

Explanation of Solution

Given: A figure is given as below:

  

In the given figure a boat crosses the 190 m wide river by travelling in west direction. But because of current it lands at Q which is 59 m away from point P. The angle and a inverse trigonometric function representing it is to be derived.

Formula used:

  $\tan \theta =\frac{\text{perpendicular}}{\text{base}}$

Calculation:

  $\begin{array}{l}\tan \theta =\frac{59}{190}\\ \Rightarrow \theta ={\tan }^{-1}\frac{59}{190}\\ \Rightarrow \theta ={17.2}^{\circ }\end{array}$