Chapter 12.8, Problem 1P

To determine

After three hours , find the distance between the planes.

Answer to Problem 1P

About 1345.6 km

Explanation of Solution

Given:

Two planes leave an airport at the same time, one flying at 300 km/h and the other at 420 km/h.The angle between their flight paths is $75°$ .

Formula Used:

Law of Cosine:

  $a^2=b^2+c^2-2bc\cos A$

  

Calculation:

One plane has speed 300 km/h , so , the distance it has travelled in 3 hours = 300(3) = 900 km

Second plane has speed 420 km/h , so , the distance it has travelled in 3 hours = 420(3) = 1260 km

Represent the situation :

  

Use Law of Cosine:

  $\begin{array}{l}a=\sqrt{{1260}^2+{900}^2-2(1260)(900)\cos 75°}\\ \Rightarrow a=\sqrt{1810641.6}\\ \Rightarrow a\approx 1345.6\end{array}$

So, the distance between the planes after 3 hours is about 1345.6 km.