GEOMETRY PLEASE HELP

Question

You leave the pier on a bearing of S 62° E and travel for 75 km. You then turn around and continue on a bearing N 28° E for 53 km. How far are you from the pier? 

Answer 1

If I understand the directions correctly, a right triangle is formed with legs 75 & 53 km so Pythagorean Theorem can be applied.

 

I made the following diagram: Pier is at Origin; direction of travel (dist = 75) is 28 degrees clockwise from due East.

At point C (for change of direction), direction is 28 degrees clockwise from due North. This distance, 53 km, terminates at point S(for Stop).

 

Using auxiliary lines and alternate interior angles, I determined that Angle C is 90 degrees.  Make the drawing and come to the same conclusion, I hope!  All you have to do is prove that Angle C = 90^o