1. **State the problem:** Eileen measures the angle of elevation to the top of a tree to be 42° from a point 27 metres away from the base. Find the height $h$ of the tree. 2. **Identify the right triangle:** The distance from Eileen to the base is the adjacent side: 27 metres. The height $h$ is the opposite side. The angle of elevation is 42°. 3. **Use trigonometry:** We use the tangent function relating opposite and adjacent sides: $$\tan(42^\circ) = \frac{h}{27}$$ 4. **Solve for $h$:** $$h = 27 \times \tan(42^\circ)$$ 5. **Calculate the value:** Using $\tan(42^\circ) \approx 0.9004$, $$h \approx 27 \times 0.9004 = 24.31$$ 6. **Round the answer:** The height of the tree to the nearest metre is $$h \approx 24 \, \text{metres}$$.