1. The problem involves Dylan using a clinometer to measure the height of a tree. 2. Dylan stands 6 m from the base of the tree and measures the angle of elevation using the clinometer. 3. The clinometer shows an angle of 42° from the vertical, which means the angle of elevation from the horizontal is $48^\circ$ because angles in a triangle sum to 180° and the right angle is 90°: $$180^\circ - 42^\circ - 90^\circ = 48^\circ$$ 4. The height of Dylan's eye above the ground is 1.6 m. 5. We model the situation as a right triangle where: - The base is 6 m (distance from Dylan to the tree) - The angle of elevation is $48^\circ$ - The vertical side from Dylan's eye to the top of the tree is unknown (let's call it $h$) 6. Using the tangent function, which relates opposite side to adjacent side in a right triangle: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 48^\circ$, opposite side is $h$, adjacent side is 6 m: $$\tan(48^\circ) = \frac{h}{6}$$ 7. Solve for $h$: $$h = 6 \times \tan(48^\circ)$$ 8. Calculate $\tan(48^\circ)$: $$\tan(48^\circ) \approx 1.1106$$ 9. Therefore: $$h = 6 \times 1.1106 = 6.6636 \text{ m}$$ 10. This $h$ is the height from Dylan's eye to the top of the tree. To find the total height of the tree, add Dylan's eye height: $$\text{Total height} = h + 1.6 = 6.6636 + 1.6 = 8.2636 \text{ m}$$ 11. Rounded to two decimal places, the height of the tree is approximately: $$8.26 \text{ m}$$ Hence, the diagram and angle interpretation are correct, and the height calculation follows logically from the given data.