Triangle A B C is shown. Angle C A B is a right angle. Angle A B C is 30 degrees and angle B C A is 60 degrees. The length of A C is 9 and the length of hypotenuse C B is 18. Which trigonometric ratios are correct for triangle ABC? Select three options.

SinB = 1/2, SinC = √3/2 and

TanC = √3

Step-by-step explanation:

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Given triangle ABC, we will use the SOH, CAH, TOA trig identity to get the correct ratio.

Given the hypotenuse BC = 18 and one of the other two sides AC = 9, we can get the third side AB using Pythagoras theorem.

BC² = AC²+AB²

18² = 9²+AB²

2² = 1²+AB²

AB² = 4-1

AB² = 3.

AB = √3

Making <ABC as reference angle, AC will be opposite and AB will be the adjacent.

Sin<ABC = opp/hyp = AC/BC

Sin<ABC = 1/2

Cos<ABC = adj/hyp = AB/BC

Cos<ABC = √3/2

Tan<ABC = opp/adj = AC/AB

Tan<ABC = 1/√3

Making <BCA as reference angle, AB will be opposite and AC will be the adjacent.

Sin<BCA = opp/hyp = AB/BC

Sin<BCA = √3/2

Cos<BCA = adj/hyp = AC/BC

Cos<BCA = 1/2

Tan<BCA = opp/adj = AC/AB

Tan<BCA = √3

Frim the above calculation, the correct options are sin<ABC = 1/2, Sin<BCA = √3/2 and Tan<BCA = √3

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step-by-step explanation: