Express sin a, cos a, and tan a as ratios

Explanation:

Sine of an angle is the ratio of the opposite side over the hypotenuse. For reference angle A, the opposite side is BC = 6sqrt(3). The hypotenuse is the longest side AB = 12

Sin(angle) = opposite/hypotenuse

sin(A) = BC/AB

sin(A) = 6sqrt(3)/12

sin(A) = sqrt(3)/2

Cosine is the ratio of the adjacent and hypotenuse

cos(angle) = adjacent/hypotenuse

cos(A) = AC/AB

cos(A) = 6/12

cos(A) = 1/2

Tangent is the ratio of the opposite and adjacent

tan(angle) = opposite/adjacent

tan(A) = BC/AC

tan(A) = 6sqrt(3)/6

tan(A) = sqrt(3)

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