If cos A = 5/13, what is the value of tan A?

If cos A = 5/13, what is the value of tan A?

Step 1: We know that cos A = 5/13.
Step 2: We need to find sin A using the identity sin²A + cos²A = 1.
Step 3: First, calculate cos²A: (5/13)² = 25/169.
Step 4: Now, substitute cos²A into the identity: sin²A + 25/169 = 1.
Step 5: To isolate sin²A, subtract 25/169 from both sides: sin²A = 1 - 25/169.
Step 6: Convert 1 to a fraction with a denominator of 169: 1 = 169/169.
Step 7: Now, subtract: sin²A = 169/169 - 25/169 = 144/169.
Step 8: Take the square root of both sides to find sin A: sin A = √(144/169) = 12/13.
Step 9: Now we have sin A = 12/13 and cos A = 5/13.
Step 10: Use the identity tan A = sin A / cos A: tan A = (12/13) / (5/13).
Step 11: Simplify the fraction: tan A = 12/5.

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