1. **State the problem:** We have a right triangle VWU with a right angle at W. Side VW = 33 units, side VU = 68 units, and we want to find $\sin(V)$, $\cos(V)$, and $\tan(V)$ for angle $V$. 2. **Identify sides relative to angle $V$:** - Opposite side to angle $V$ is $WU$ (unknown). - Adjacent side to angle $V$ is $VW = 33$. - Hypotenuse is $VU = 68$. 3. **Find the missing side $WU$ using the Pythagorean theorem:** $$WU = \sqrt{VU^2 - VW^2} = \sqrt{68^2 - 33^2} = \sqrt{4624 - 1089} = \sqrt{3535}$$ 4. **Simplify $\sqrt{3535}$ if possible:** Factor 3535: $3535 = 5 \times 707 = 5 \times 7 \times 101$ (no perfect squares), so $WU = \sqrt{3535}$ remains as is. 5. **Write the trigonometric ratios:** - $\sin(V) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{WU}{VU} = \frac{\sqrt{3535}}{68}$ - $\cos(V) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{VW}{VU} = \frac{33}{68}$ - $\tan(V) = \frac{\text{opposite}}{\text{adjacent}} = \frac{WU}{VW} = \frac{\sqrt{3535}}{33}$ 6. **Final answers:** $$\sin(V) = \frac{\sqrt{3535}}{68}$$ $$\cos(V) = \frac{33}{68}$$ $$\tan(V) = \frac{\sqrt{3535}}{33}$$ These are simplified exact values for the sine, cosine, and tangent of angle $V$.