I NEED HELP ON THIS TRIG PROBLEM!! PLEASE!?

For reference:

a = angle at Pine knob

b = angle at Colt Station

c = angle at the Fire

A = Distance of Fire to Colt Station

B = Distance of Pine Knob to Fire

C = Distance from Pine Knob to Colt Station

To start, I'd find all the angles in the triangle. Angle a is the easiest. Since the difference in angle between B and C is 80 - 65 degrees, a = 15 degrees.

To find c, you know that one side of the angle is 70 degrees, and just have to find the other side. Since the vertical lines at Pine Knob and Colt Station are parallel and intersect the same line (i.e., C), the angles are alternate interior angles of a transversal, and thus equal. b therefore = 65 deg + 70 deg. b = 135 deg.

Angle c then becomes easy as the sum of angles in a triangle = 180. 180 = 15 + 135 + c. c = 30 degrees.

Law of sines states that A/SIN A = B/SIN b = C/SIN c

As we know both c and C, we can determine the length for each side:

30/SIN 30 = A/SIN 15 = B/SIN 135

60 = A/0.2588 = B/0.7071

A = 15.528 km

B = 84.854 km

To be honest I have absolutely no idea.

I tried to figure it out and couldn't. I'd just leave it blank and ask in class (if you teacher allows to go over questions)

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