A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60° to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the cable.

To find the height of the balloon from the ground, we can use trigonometry. We know that the cable is inclined at a 60° angle to the horizontal and has a length of 200 m.

The height of the balloon (opposite side) can be found using the sine function:

\[
\sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}}
\]

In this case:

\[
\sin(60°) = \frac{\text{height}}{200 \text{ m}}
\]

Solving for the height:

\[
\text{height} = 200 \text{ m} \times \sin(60°)
\]

The value of \(\sin(60°)\) is \(\frac{\sqrt{3}}{2}\), so:

\[
\text{height} = 200 \text{ m} \times \frac{\sqrt{3}}{2} = 100\sqrt{3} \text{ m}
\]

Therefore, the height of the balloon from the ground is \(100\sqrt{3}\) meters.