1. **State the problem:** We have a right triangle with angles 64° and 32°, and the base length is 6.4 meters. We need to find the height $u$ and the hypotenuse $v$. 2. **Recall the triangle angle sum rule:** The sum of angles in a triangle is 180°. Since the triangle is right-angled, the right angle is 90°, so the other two angles are 64° and 32°. 3. **Identify sides relative to angle 64°:** - Base (adjacent to 64°) = 6.4 m - Height $u$ (opposite to 64°) - Hypotenuse $v$ 4. **Use trigonometric ratios:** - $\tan(64^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{u}{6.4}$ - $\cos(64^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{6.4}{v}$ 5. **Calculate $u$:** $$u = 6.4 \times \tan(64^\circ)$$ Using $\tan(64^\circ) \approx 2.0503$, $$u = 6.4 \times 2.0503 = 13.12$$ meters 6. **Calculate $v$:** $$v = \frac{6.4}{\cos(64^\circ)}$$ Using $\cos(64^\circ) \approx 0.4384$, $$v = \frac{6.4}{0.4384} = 14.60$$ meters **Final answers:** - Height $u = 13.12$ meters - Hypotenuse $v = 14.60$ meters