Triangle FUN has <F = 42, UN = 14, and NF = 19. What is <N to the nearest tenth
of a degree?
A) 72.8
B) 65.2
C) 72.7
D) 65.3
This is a practice problem for a Mu Alpha Theta competition. We are able to solve it with a calculator, but the directions say to solve it with paper and pencil is 2 minutes or less. We would appreciate any insights you have to help us solve it without a calculator.

Thanks very much!



I can't help, but I can offer two comments:

  1. Any approximation technique that one uses would have to be accurate to 4 decimal places: if you add .005 to the correct answer you get a number that rounds to 62.3 degrees, which is the incorrect response D. That means one would have to use exact numbers, which I don't see how to do starting with 42 degrees and ending with 62.5.

  2. The solution is not unique -- 114.8 degrees is also a possible value for angle N.

I wonder if somebody has misinterpreted the precise problem.