1. **State the problem:** We have a triangle PQR with point T on side PR such that QT is perpendicular to PR. Given PR = 10 m, QT = 7 m, and angle PQT = 40°, we need to find the length TR. 2. **Identify the right triangle:** Since QT is perpendicular to PR, triangle PQT is a right triangle with right angle at T. 3. **Use trigonometric ratios:** In right triangle PQT, angle PQT = 40° and QT = 7 m (opposite side to angle PQT). We want to find TR, which is adjacent to angle PQT. 4. **Apply the tangent function:** \[ \tan(40^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{QT}{TR} \] 5. **Solve for TR:** \[ TR = \frac{QT}{\tan(40^\circ)} = \frac{7}{\tan(40^\circ)} \] 6. **Calculate the value:** Using a calculator, \( \tan(40^\circ) \approx 0.8391 \), so \[ TR \approx \frac{7}{0.8391} \approx 8.34 \text{ m} \] 7. **Check the length:** Since PR = 10 m and T lies on PR, TR must be less than or equal to 10 m, which it is. **Final answer:** \[ TR \approx 8.34 \text{ m} \]