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

Answer

Step-by-step explanation: