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Hearing and Distance Two planes take off at the same time from an airport. The first plane is flying at 255 miles per hour on a bearing of S 45.0 ° E. The second plane is flying in the direction S 45.0 ° W at 275 miles per hour. If there are no wind currents blowing, how far apart are they after 2 hours? What is the bearing of the second plane from the first after 2 hours?

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Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
Publisher: Cengage Learning
ISBN: 9781305652224
BuyFindarrow_forward

Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
Publisher: Cengage Learning
ISBN: 9781305652224
Chapter 2.5, Problem 18PS
Textbook Problem
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Hearing and Distance Two planes take off at the same time from an airport. The first plane is flying at 255 miles per hour on a bearing of S 45.0° E. The second plane is flying in the direction S 45.0 ° W at 275 miles per hour. If there are no wind currents blowing, how far apart are they after 2 hours? What is the bearing of the second plane from the first after 2 hours?

To determine

To find:

How far apart are the two planes after 2 hours if there are no wind currents blowing and what is the bearing of the second plane from the first plane after 2 hours.

Explanation of Solution

Given information:

Two planes take off from an airport at the same time. The first plane is flying at 255 miles per hour on a bearing of S45.0°E. The second plane is flying in the direction S45.0°W at 275 miles per hour.

Sketch:

Let’s first draw the sketch of the given situation as shown below;

Now after 2 hours, let the first plane be at point C and second plane be at point B in the above diagram.

Calculation:

Now we know that,

InΔBAC,BAC=BAD+DAC=45°+45°=90°Therefore,ΔBACisarightangletriangle

Now, since the first plane is flying with a speed of 255 miles per hour therefore by using the distance formula we shall calculate the distance travelled by the first plane in 2 hours as given below;

Distance=Speed×TimeAC=255×2=510

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Trigonometry (MindTap Course List)
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