Answer:
cot(A) = 1/√3 = (√3)/3
Explanation:
The mnemonic SOH CAH TOA reminds you that the tangent relationship is ...
Tan = Opposite/Adjacent
The definition of the cotangent is ...
Cot = 1/Tan
Combining these relations, we see that ...
Cot = Adjacent/Opposite
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The side adjacent to angle A is AC. It is marked as having length 3. The side opposite angle A is BC. It is marked as having length 3√3. Then the cotangent ratio is ...
cot(A) = AC/BC = 3/(3√3)
cot(A) = 1/√3 = (√3)/3
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Comment on the form of the answer
Some folks insist on the denominator being rationalized (no roots); others don't care. Use the form that pleases your grader.