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A 30-60-90 triangle with a hypotenuse of 6 . Find the length of all other sides

User Husky
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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
User Vito Liu
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