An English pig farmer successfully sued a hot air ballon company, which allegedly flew a low-flying balloon too close to the pig farm.

The case revolved around the height of the balloon as it flew over the farm, as it is against the law for a flying object to float at a height below 1500 feet. The company cited GPS data, claiming that they were more than 2500 feet away.

Based on a photograph that was taken of the balloon flying over the field, and a laser rangefinder to determine the exact height of the trees, Professor Chris Fewster managed to use trigonometry and bearing to determine the tilt of the camera, and then the distance of the balloon.

Prof Fewster said: "The wonderful thing about mathematics is that it helps us think clearly about the world. This case shows how even relatively simple mathematics like trigonometry can make an important contribution.

The formula that as used to calculate the tilt and height is

\[ \tan \alpha = \frac{ ( Z _ t - H ) f Q - R_t q_t h } { R_t Q f + ( Z_t - H) q_t h } \]

Any guesses to what these terms are, or how to do such a calculation in future?

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