Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?

The balloon is between Caleb and Emily, so the horizontal distances from them to the point directly below the balloon add to 100 yards. For a 45° angle, Caleb’s horizontal distance is h/tan(45°) = h; for a 60° angle, Emily’s is h/tan(60°) = h/√3. Thus h + h/√3 = 100, giving h ≈ 63.4 yards. The balloon is approximately 63.4 yards off the ground, choice B.

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