Pigs need math too!

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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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$