To find the distance between Dimitri and Sarah, we can use trigonometry and the given information about the angle and length of the kite string.
Let's assume that Sarah is standing at point A directly below the kite, and Dimitri is standing at point B where he is holding the kite string. The distance between Dimitri and Sarah can be represented as the horizontal distance from point B to point A.
In the given scenario, we have the following information:
- The length of the kite string (hypotenuse): 40m
- The angle between the kite string and the horizontal ground: 72°
We can use the trigonometric function cosine to calculate the horizontal distance. The cosine of an angle is defined as the adjacent side length divided by the hypotenuse.
Cos(72°) = adjacent side / 40m
Rearranging the formula to solve for the adjacent side length:
adjacent side = Cos(72°) * 40m
Calculating the adjacent side length:
adjacent side = 0.309 * 40m
adjacent side ≈ 12.36m
Therefore, the distance between Dimitri and Sarah is approximately 12.36 meters.