Solved: "Label the words of this 30,60,90 right triangle..."

Clifland

Answered question

2021-03-05

Label the words of this 30,60,90 right triangle

S L, 2 S L, and S L \sqrt{2}

Elberte

Skilled2021-03-06Added 95 answers

From the right triangle ABC, we have

∴ \sin (A) = \frac{B C}{A C}

\Rightarrow \sin (30^{\circ}) = \frac{v}{6}

\Rightarrow 1 = \frac{v}{3}

\Rightarrow v = 3

From the right triangle ABC, we have

∴ \cos (A) = \frac{A B}{A C}

\Rightarrow \cos (30^{\circ}) = \frac{u}{6}

\Rightarrow \frac{\sqrt{3}}{2} = \frac{u}{6}

\Rightarrow \sqrt{3} = \frac{u}{3}

\Rightarrow u = 3 \sqrt{3}

Since, the sum of all angles of a triangle is

180^{\circ}

∴ ∠ A + ∠ B + ∠ C = 180^{\circ}

\Rightarrow 30^{\circ} + 90^{\circ} + ∠ C = 180^{\circ}

\Rightarrow 120^{\circ} + ∠ C = 180^{\circ}

\Rightarrow ∠ C = 60^{\circ}

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