Question

You’re observing a hot air balloon from a spot 1.8 miles away from where it lifted off (remember 1 mile=5280 feet). If the balloon is currently 2500 ft in the air, at what angle of elevation would you have to look in order to be pointed at it?

Answer 1

Answer: Approximately 14.737627 degrees

Round this however you need to

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Step-by-step explanation:

Refer to the diagram below.

1 mi = 5280 ft

1.8 mi = 1.8*5280 ft

1.8 mi = 9504 ft

We use the tangent ratio to tie together the opposite side (2500 ft) with the adjacent side (9504 ft)

tan(angle) = opposite/adjacent

tan(x) = 2500/9504

x = arctan(2500/9504)

x = 14.737627 approximately

Side note: the arctangent is the same as inverse tangent denoted as
`\tan^(-1)`