If sin(θ) = 5/13 and θ is an acute angle, find cos(θ).

Use the Pythagorean trigonometric identity:
sin²(θ) + cos²(θ) = 1

We are given:
sin(θ) = 5/13

Substitute this value into the identity:
(5/13)² + cos²(θ) = 1

Square the fraction:
25/169 + cos²(θ) = 1

Write 1 as 169/169:
25/169 + cos²(θ) = 169/169

Subtract 25/169 from both sides:
cos²(θ) = 144/169

Take the square root:
cos(θ) = ±12/13

Because θ is acute, it lies in Quadrant I, where cosine is positive.

Therefore:
cos(θ) = 12/13.