Solving a Problem with Bearing 
A plane flies 1.3 hr at 110mph on a bearing of 38 degrees. It then
  turns and flies 1.5 hr at the same speed on a bearing of 128 degrees.
  How far is the plane from its starting point?

To solve this, I have drawn a rough sketch. I have also labeled the appropriate sides at 143 miles (distance = rate * time; 1.3hr * 110mph) and 165 miles (1.5hr * 110mph).
But I am having a difficult time concluding which angle within the sketch is the 90 degree angle to allow me to use a trigonometric function or the Pythagorean theorem to solve it. 
Edit: It is really important for me to know how to determine the measure of any angle that can be inferred. Not only because I am expecting the professor to attempt to fool us by providing measures where the triangle in question is not a right triangle, but because I thought I had already mastered this skill previously. 

Since you turn a total of $90^{\circ}$ the path of the plane forms a right triangle and the two given paths are the legs.
Using pythagorean $a^2+b^2=c^2$, where here $a=1.3\cdot 110=143$ and $b=1.5\cdot 110=165$, so $c=\sqrt{(1.3\cdot 110)^2+(1.5\cdot 110)^2} = 218.344 \text{ mi}$

