1. **State the problem:** We have a right triangle WUV with right angle at U, legs WU = 48 and UV = 36, and hypotenuse WV = 60. We need to express the trigonometric ratios for angle W as fractions in simplest terms. 2. **Recall the definitions of trig ratios for angle W:** - \(\sin W = \frac{\text{opposite}}{\text{hypotenuse}}\) - \(\cos W = \frac{\text{adjacent}}{\text{hypotenuse}}\) - \(\tan W = \frac{\text{opposite}}{\text{adjacent}}\) 3. **Identify sides relative to angle W:** - Opposite side to W is UV = 36 - Adjacent side to W is WU = 48 - Hypotenuse is WV = 60 4. **Calculate each ratio:** \[ \sin W = \frac{36}{60} = \frac{\cancel{36}}{\cancel{60}} = \frac{3}{5} \] \[ \cos W = \frac{48}{60} = \frac{\cancel{48}}{\cancel{60}} = \frac{4}{5} \] \[ \tan W = \frac{36}{48} = \frac{\cancel{36}}{\cancel{48}} = \frac{3}{4} \] 5. **Final answer:** - \(\sin W = \frac{3}{5}\) - \(\cos W = \frac{4}{5}\) - \(\tan W = \frac{3}{4}\)