Question

There are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle. If the hot air balloon is 15 feet off the ground, what is the distance between the two ropes rounded to the nearest hundredth of a foot?

Answer 1

i) For the 45° triangle
tan Ө = opposite / adjacent
tan Ө = height of the balloon off the ground / x
tan 45° = 15 / x
x = 15 / tan 45°
x = 15 / 1
x = 15

ii) For the 30°
tan Ө = opposite / adjacent
tan Ө = height of the balloon off the ground / y
tan 30° = 15 / y
y = 15 / tan 30°
y = 15/ 0.577350
y = 25.9808

Distance between the ropes = x + y = 15 + 25.9808 = 40.9808

:. Therefore the distance between the two balloon mooring ropes is 40.98 feet
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