Discussion
A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60º to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the c
Answer: C
The cable has no slack, so it is a straight hypotenuse of 200 m, and the balloon's height is the side opposite the \( 60^{\circ} \) inclination.
\[ \sin 60^{\circ} = \frac{h}{200} \]
\[ h = 200 \times \frac{\sqrt{3}}{2} = 100\sqrt{3} = 173.2 \text{ m} \]
The cable length is a slant distance, so sine applies, not tangent. The height must come out below 200 m, which rules out anything larger on inspection.
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