If tan θ = $\dfrac{5}{12}$ and θ is acute, find the values of sin θ and cos θ.

tan θ = $\dfrac{\text{perpendicular}}{\text{base}} = \dfrac{5}{12}$

Let perpendicular = 5x and base = 12x

By pythagoras theorem, we get :

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = (12x)² + (5x)²

Hypotenuse² = 144x² + 25x²

Hypotenuse² = 169x²

Hypotenuse = $\sqrt{169x^2}$

Hypotenuse = 13x

sin θ = $\dfrac{\text{perpendicular}}{\text{hypotenuse}} = \dfrac{5x}{13x} = \dfrac{5}{13}$

cos θ = $\dfrac{\text{base}}{\text{hypotenuse}} = \dfrac{12x}{13x} = \dfrac{12}{13}$