60.6k views
3 votes
A 30-60-90 triangle with a hypotenuse of 6 . Find the length of all other sides

User Husky
by
7.5k points

1 Answer

4 votes
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
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories