   Chapter 5.5, Problem 26E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Mara’s boat leaves the dock at the same time that Meg’s boat leaves the dock. Mara’s boat travels due east at 12 mph. Meg’s boat travels at 24 mph in the direction N 30 ° E. To the nearest tenth of mile, how far apart will the boats be in half an hour? To determine

To find:

The distance between the boats after half an hour.

Mara’s boat left the dock at the same time that Meg’s boat left the dock. Maras boat travelled due east at 12 mph and Meg’s boat travelled at 24 mph in the direction N30°E.

Explanation

Approach:

For a right triangle, for which the measure of the interior angles 30°, 60°, and 90°; if ‘a’ is the length of measure of the shorter leg; opposite to the angle 30°, then the length of the other two sides is given by

Length of the longer leg (opposite to 60°) =a3

Length of the hypotenuse (opposite to 90°)=2a.

In general

Length of the longer leg =3× (Length of the shorter leg)

Length of the hypotenuse =2× (Length of the shorter leg)

Calculation:

Given,

 Mara’s boat Meg’s boat Speed 12 mph 24 mph Direction East N30°E

Distance travelled by Maras boat in half an hour =6 mi.

Distance travelled by Megs boat in half hour =12 mi.

Let OT=6 mi., and

OG=12 mi.

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