A plane flying at 1000 meters above the ground fires a laser at an angle of 60 degrees downwards. How far does the light travel to reach the ground?

To solve the problem, first, you need to understand that the laser beam forms a right triangle with the ground. The height of the plane above the ground is the opposite side, and the distance the light travels forms the hypotenuse of this triangle.

When the laser is fired at an angle of 60 degrees downwards, you can use trigonometric relationships to find the distance the light travels. Specifically, you use the sine function, which relates the angle to the opposite side (height) and the hypotenuse (the distance traveled by the light).

Using the sine function: [ \sin(60^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1000 \text{ meters}}{d} ] Solving for (d) (the distance traveled by the light): [ d = \frac{1000 \text{ meters}}{\sin(60^\circ)} ] Since (\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866), the calculation becomes: [ d \approx \frac{1000 \text{ meters}}{0.866}