Monday, October 31, 2016

Halloween Challenge

Here's a spooky problem in trigonometry.

Triangle ABC has area 780 square units. Side c is 78 units long. Angles A and B satisfy

cot(A) − cot(B) = 6.

Find the lengths of sides a and b and the measures of all three angles.

(In keeping with the spirit of the holiday, I tried to make this as nasty-sounding as possible.)

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