Solving a Trig Story Problem: Ft. Myers to Orlando

[starchild75]

Homework Statement

An airplane flies from Ft. Myers to Sarasota, a distance of 150 miles, and then turns thru an angle of 50 degrees, and flies to Orlando, a distance of 100 miles. How far is it from Fort Myers to Orlando?

Homework Equations

Law of Cosines. c^2= a^2 + b^2-2ab cos gamma

The Attempt at a Solution

Using the law of cosines, I squared 150 and added 100 squared. I then subtracted 100 times 150 times cosine of 50 degrees. I then took the square root of c. I got an answer of 114 miles, which cannot be true, having driven in Florida, and also because the diagram shows the route as the hypotenuse. What am I doing wrong?

 

[cristo]

I suspect the problem is with your angle. Which angle on the diagram is 50 degrees?-- I don't think it's the internal one!

 

[starchild75]

the plane flies north from fort myers to sarasota, then turns 50 degrees to the right, north east toward orlando. Is it the "turning thru an angle" that changes the problem?

 

[cristo]

the plane flies north from fort myers to sarasota, then turns 50 degrees to the right, north east toward orlando.

OK, so the angle 50 degrees is measured from the northerly direction to the direction in which it flies to get to orlando. How do you find out the interior angle of the triangle (i.e. the angle from the southerly direction to the direction in which the plane flies from saratosa to orlando)? This is the angle you need to use the cosine rule.

 

[starchild75]

130 degrees? this gives me an answer of approximately 227.6 miles.?? In looking at the diagram now, it is clear that the turn creates an obtuse angle.

 

[cristo]

Yup, that's what I get.

 

[starchild75]

awesome, thanks.