A hot-air balloon at a festival in Bikaner rises vertically from a point on the ground that is 40 m from where Karan is standing. The angle of elevation of the balloon from Karan first measures 30° and a little later measures 60°. Find the exact distance (in m) the balloon has risen between the two observations.

Question

Accepted Answer

80√3. First height: tan 30 = h1/40 => h1 = 40√3 m. Later: tan 60 = h2/40 => h2 = 40 √3 m. Risen = 40 √3 - 40√3 = 120 - 40√3 = 80√3 m (about 46.19 m). The value 40 √3 m is only the final height.

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