SOLUTION: The distance between Miami and Orlando is about 220 miles. A pilot flying from Miami to Orlando starts the flight 10degrees off course to avoid a storm. If the pilot adjusts his co

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Question 1210282: The distance between Miami and Orlando is about 220 miles. A pilot flying from Miami to Orlando starts the flight 10degrees off course to avoid a storm. If the pilot adjusts his course after 100 miles, how much farther is the flight than a direct route?
Found 2 solutions by ikleyn, mccravyedwin:
Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.
The distance between Miami and Orlando is about 220 miles. A pilot flying from Miami to Orlando
starts the flight 10 degrees off course to avoid a storm. If the pilot adjusts his course
after 100 miles, how much farther is the flight than a direct route?
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let point M represents Miami, point O represents Orlando, and let point C represents
the point where the pilot adjusts/changes the course.


So, we have triangle MOC on a plane (surely, we consider the Earth surface as flat
in this problem).


In triangle MOC, side MO is 220 miles (the distance from Miami to Orlando);
side MC is 100 miles (given) and the concluded angle OMC is 10 degrees.


Let's apply the cosine law to find the side CO of this triangle.  We have then


    CO = sqrt%28220%5E2%2B100%5E2-2%2A220%2A100%2Acos%2810%5Eo%29%29 = sqrt%28220%5E2%2B100%5E2-2%2A220%2A100%2A0.98481%29 = 122.753 miles (rounded).


The problem asks how longer is the sum MC + CO  than MO.  So, we calculate

    MC + CO - MO = 100 + 122.753 - 220 = 2.753 miles.


ANSWER.  The flight is 2.753 miles longer than the direct root.

Solved.

Thanks for posting this problem.

I appreciate the accuracy of your post and clear language of your message.

It is a rare case in our days.



Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!



Point M represents Miami, point O represents Orlando.
Point A represents the point at which the pilot adjusted his path
directly toward Orlando,

The red path is his actual flight.
The green path is the direct route.

we find x in triangle MAO:

We have SIDE-ANGLE-SIDE given, so we use the law of cosines:

x%5E2=100%5E2%2B220%5E2-2%28100%29%28220%29cos%2810%5Eo%29
x%5E2=15068.45887
x=122.7536511

His flight path is 100 + x = 100 + 122.7536511 = 222.7536511
So his flight was 222.7536511 - 220 =  2.753651147 miles farther than
the direct route.   Round off as you were instructed.

Edwin