First, we can use Thales' Theorem to determine that because AC is along the circle's diameter, angle B (the angle opposite to that side) is a right angle.
Next, we know that an inscribed angle with its vertex on the circle, formed by two intersecting chords (A in this case) is equal to 1/2 of its intercepted arc, so angle A = 70/2=35
We can then use the fact that a triangle adds up to 180 degrees here to get
there for at 8 hikes with either deal it would be the same but if you went up a number of hikes for the first option it would only be $43.00 spent in total. but with the second option it would be $45.00.
