Angles A and B are complementary angles in a right triange. The value of cos (A) is 12/13. What is the value of Tan (A)

Using the pythagorean identity, we can find the value of sin (A)

cos^2 (A) + sin^2 (A) = 1

(12/13) ^2 + sin^2 (A) = 1

144/169 + sin^2 (A) = 1

sin^2 (A) = 1 - 144/169

sin^2 (A) = 169/169 - 144/169

sin^2 (A) = (169 - 144) / 169

sin^2 (A) = 25/169

sin (A) = sqrt (25/169)

sin (A) = 5/13

Which is then used to find tan (A)

tan (A) = sin (A) / cos (A)

tan (A) = (5/13) divided by (12/13)

tan (A) = (5/13) * (13/12)

tan (A) = (5*13) / (13*12)

tan (A) = 5/12

The final answer is 5/12