1. **State the problem:** We need to find the length $r$ in a right triangle where one leg is 1.95 m, and the angles adjacent to this leg are 48° and 37°. 2. **Identify the triangle properties:** The triangle has a right angle, and the angles given are 48° and 37°, which sum to 85°. The remaining angle is 90°, confirming a right triangle. 3. **Assign sides:** The side of length 1.95 m is adjacent to the 48° angle. The length $r$ is the hypotenuse opposite the right angle. 4. **Use trigonometry:** Using the cosine of 48°, $$\cos 48^\circ = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{1.95}{r}$$ 5. **Solve for $r$:** $$r = \frac{1.95}{\cos 48^\circ}$$ 6. **Calculate the value:** $$\cos 48^\circ \approx 0.6691$$ $$r = \frac{1.95}{0.6691} \approx 2.91$$ 7. **Final answer:** The length $r$ is approximately **2.91 m** to 2 decimal places.