Question

Hi. This is the question:
A jet flew 140 mi on a course of 196 degrees and then 120 mi on a course of 106 degrees then the jet return to its starting point via the shortest route possible. Find the total distance that the jet traveled.
I found the answer for this. It's this one:
http://ph.answers.yahoo.com/question/index?qid=20110828043233AAVgQcy
Now I understand everything else, ut my problem is why they used the given angles to confirm that it is a right triangle? I know this has something to do with theorems on parallel lines, but I just can't to picture how. Illustrations are greatly appreciated. (It will actually be a lot easier for me to understand this question). Thank you.

Answer 1

The plane flew 140 mi on some course and then turned by 90 degrees and flew 120 mi. To find total distance the plane flew we need to find the remaining third side of the triangle.

Since the triangle is right the third side may be found using the Pythagoras theorem:

$$c ^ {2} = a ^ {2} + b ^ {2}$$

Here $c$ is unknown side, $a = 140, b = 120$ . So

$$c = \sqrt {a ^ {2} + b ^ {2}} = 1 8 4. 3 5$$

So total distance equals

$$a + b + c = 1 4 0 + 1 2 0 + 1 8 4. 3 5 = 4 4 4. 3 5$$