Chapter 12.6, Problem 6P

To determine

To determine the angle between the courses of two cruise ship.

Answer to Problem 6P

Angle between them is ${49.4}^{\circ }$

Explanation of Solution

Given information :

Given speed are 10mi/h and 25 mi/h

Two hours later they are 40 mi apart.

Distance travelled by both in 2 hrs.

First cruise ship travelled 20 mi.

Second cruise ship travelled 50 mi.

  

Here we shall use the cosine rule.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Put the values, we get,

  $\begin{array}{l}\cos A=\frac{{20}^2+{50}^2-{40}^2}{2\left(20\right)\left(50\right)}\\ \cos A=\frac{1300}{2000}\\ A={\cos }^{-1}0.65\\ A={49.4}^{\circ }\end{array}$

Angle between them is ${49.4}^{\circ }$