1. Find the "opposite side," if the angle is 60 degrees and the hyp is 6:
opp opp sqrt(3)
sin 60 deg = ------- = -------- = ----------
hyp 6 2
Cross-multiplying, 2(opp) = 6sqrt(3), so that opp = 3 sqrt(3) (answer)
2. Use the Pyth. Thm. to find the "adjacent side:"
[3sqrt(3)]^2 + x^2 = 6^2, or 9(3) + x^2 = 36, or x^2 = 9, or x = 3.
The lengths of the legs of this 30-60-90 triangle are 3 and 3 sqrt(3).
check: Does 3^2 + [3sqrt(3)]^2 = 6^2?
Does 9 + 9(3) = 6^2? YES