1. **Stating the problem:** We have a right triangle with a vertical leg of length 21 km and an angle of 142° given. We want to find the length of the hypotenuse or other sides if needed. 2. **Understanding the angle:** Since the triangle is right-angled, the angle inside the triangle adjacent to the vertical leg cannot be 142° because angles in a triangle sum to 180°. The 142° likely refers to a bearing or external angle. 3. **Interpreting the angle:** The angle 142° can be interpreted as the bearing from the north line, so the angle inside the triangle adjacent to the vertical leg is $180^\circ - 142^\circ = 38^\circ$. 4. **Using trigonometry:** The vertical leg is opposite the angle of $38^\circ$. Let the hypotenuse be $h$. 5. **Applying sine function:** $\sin(38^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{21}{h}$. 6. **Solving for hypotenuse:** $$ h = \frac{21}{\sin(38^\circ)} $$ 7. **Calculating the value:** Using $\sin(38^\circ) \approx 0.6157$, $$ h \approx \frac{21}{0.6157} \approx 34.1 \text{ km} $$ **Final answer:** The hypotenuse length is approximately $34.1$ km.