1. Problem statement: Jimmy is on a ship 708 meters away from the base of a cliff. The angle of elevation from Jimmy to the top of the lighthouse on the cliff is $26^\circ$. 2. We want to find the height of the lighthouse above the base of the cliff. 3. Use trigonometry: In the right triangle formed by Jimmy, the cliff base, and the lighthouse top, the distance from Jimmy to the cliff base is the adjacent side, and the lighthouse height is the opposite side. 4. The tangent of the angle of elevation relates opposite and adjacent sides: $$\tan(26^\circ) = \frac{\text{height}}{708}$$ 5. Solve for height: $$\text{height} = 708 \times \tan(26^\circ)$$ 6. Calculate the tangent value: $$\tan(26^\circ) \approx 0.4877$$ 7. Multiply to find height: $$\text{height} \approx 708 \times 0.4877 = 345.2 \text{ meters}$$ Answer: The height of the lighthouse above the base of the cliff is approximately 345.2 meters.