1. **State the problem:** Calculate the height of the flagpole (FP) and the length of one of the ropes (PR) holding the flagpole. 2. **Find the height FP:** Given a right triangle with hypotenuse $18$ m and angle $38^\circ$ at point G, the height FP is the side opposite the angle. 3. **Use the sine function:** $$\sin(38^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{FP}{18}$$ 4. **Solve for FP:** $$FP = 18 \times \sin(38^\circ)$$ 5. **Calculate FP:** $$FP \approx 18 \times 0.6157 = 11.1$$ 6. **Find the length PR of the rope:** PR is the hypotenuse of the right triangle with legs $18$ m (hypotenuse of original triangle) and $9.7$ m (adjacent side). 7. **Use Pythagoras theorem:** $$PR = \sqrt{(18)^2 + (9.7)^2}$$ 8. **Calculate PR:** $$PR = \sqrt{324 + 94.09} = \sqrt{418.09} \approx 20.44$$ **Final answers:** - Height of flagpole $FP \approx 11.1$ m - Length of rope $PR \approx 20.44$ m