1. **Problem statement:** We are given a right triangle where \( \tan \theta = 0.75 \) and the lengths of the two sides adjacent to the right angle are single-digit whole numbers. We need to find the length of the third side. 2. **Recall the definition of tangent:** \[ \tan \theta = \frac{\text{opposite side}}{\text{adjacent side}} \] This means the ratio of the opposite side to the adjacent side is 0.75. 3. **Express the ratio as a fraction:** \[ 0.75 = \frac{3}{4} \] So the opposite side is 3 units and the adjacent side is 4 units (both single-digit whole numbers). 4. **Use the Pythagorean theorem to find the hypotenuse:** \[ \text{hypotenuse} = \sqrt{(\text{opposite})^2 + (\text{adjacent})^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} \] 5. **Simplify the square root:** \[ \sqrt{25} = 5 \] 6. **Conclusion:** The length of the third side (the hypotenuse) is 5 units. This matches the given triangle with sides 3, 4, and 5.