Answer:
(a) sin⁻¹(√35/14)
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relations between sides and angles in a right triangle. Here, the given sides AB and AC are the side opposite angle C, and the hypotenuse (opposite right angle B). That means the relevant relation is ...
Sin = Opposite/Hypotenuse
sin(C) = AB/AC
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For this problem, substituting values gives ...
sin(C) = (3√5)/(6√7) = (1/2)√(5/7) = (1/2)(√35)/7 = (√35)/14
C = arcsin((√35)/14)
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<em>Additional comment</em>
Choice B can be eliminated on the grounds that the fraction is not reduced to lowest terms. Choices C and D are eliminated because they assume a cosine relation is involved. That is, you can choose the correct answer based on SOH CAH TOA without concerning yourself with the details of the radical expression.
