Problem:
From the Pedimaxus International Airport a tour helicopter can fly to Cliffs of Insanity Point by following a bearing of N8.9°E for 192 miles and it can fly to Bigfoot Falls by following a bearing of S63.4°E for 207 miles. Cliffs of Insanity Point and Bigfoot Falls both lie on a straight stretch of the Great Sasquatch Canyon. What bearing would the tour helicopter need to follow to go directly from Bigfoot Falls to Cliffs of Insanity Point?
Ok, after a few days I have come up with the answer.
With the given measurements, we can create a triangle. After this, if we construct two right triangles under and above the main triangle, we can find a way to solve x° like this: Setup 2. We can get 26.6° since we already know the other two angles of the right triangle. From this we need to find two values in order to find the bearing, shown in this image: Setup 3. Side c can be found with the law of cosines, and comes to be approximately 322.304. Now, the law of sines can be used to find the angle measure of angle C with this equation: $$ \frac{sin(107.7°)}{322.304}= \frac{sin(C°)}{192}$$ This comes to approximately 34.6°. After looking at the image of Setup 3, we see that we know two out of three angles, and since we know these three angles must equal 90°, we can subtract the sum of the two known angles to get 28.8° as the angle measurement for x°. However, since we need to get the bearing, we must put this in bearing form, and since the angle is in quadrant 2, the final answer is N28.8°W.