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in the 30-60-90 triangle below, side \\(s\\) has a length of \\(\\under…

Question

in the 30-60-90 triangle below, side \\(s\\) has a length of \\(\underline{\quad\quad}\\) and side \\(r\\) has a length of \\(\underline{\quad\quad}\\).

a. \\(6\\), \\(12\sqrt{3}\\)
b. \\(6\sqrt{2}\\), \\(6\sqrt{2}\\)
c. \\(12\sqrt{3}\\), \\(24\\)
d. \\(24\sqrt{3}\\), \\(6\\)
e. \\(6\\), \\(6\sqrt{3}\\)
f. \\(12\sqrt{3}\\), \\(12\sqrt{3}\\)

Explanation:

Identify given values

Using the 30-60-90 Triangle Properties knowledge point

$$ LATEXBLOCK0 $$

Calculate short leg s

Using the 30-60-90 Triangle Properties knowledge point

$$ LATEXBLOCK1 $$

Calculate long leg r

Using the 30-60-90 Triangle Properties knowledge point

$$ LATEXBLOCK2 $$

Answer:

  • A. \(6\), \(12\sqrt{3}\)
  • B. \(6\sqrt{2}\), \(6\sqrt{2}\)
  • C. \(12\sqrt{3}\), \(24\)
  • D. \(24\sqrt{3}\), \(6\)
  • E. \(6\), \(6\sqrt{3}\) (Correct answer)
  • F. \(12\sqrt{3}\), \(12\sqrt{3}\)