Question

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. sin(C) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction cos(B) = StartFraction StartRoot 2 EndRoot Over 3 EndFraction tan(C) = StartRoot 3 EndRoot sin(B) = One-half tan(B) = StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction

Answer 1

Answer:

The answer is A C and D on Edge 2020

Step-by-step explanation:

Answer 2

Answer:

i. sin(C) = $\frac{\sqrt{3} }{2}$

ii. tan(C) = $\sqrt{3}$

iii. sin(B) = $\frac{1}{2}$

Step-by-step explanation:

Given a right angled triangle ABC, with a right angle at A.

<ABC = $30^{0}$

<BCA = $60^{0}$

AC = 9 = 1

CB = 18 = 2

Applying Pythagoras theorem to ΔABC, we have;

AB = $\sqrt{BC^{2} - AC^{2} }$

    = $\sqrt{2^{2} - 1^{2} }$

   = $\sqrt{3}$

Thus applying the trigonometric ratios, it would be observed that;

i. sin(C) = $\frac{\sqrt{3} }{2}$

ii. tan(C) = $\sqrt{3}$

iii. sin(B) = $\frac{1}{2}$