PLeeeeeeaaaassseeee help, its very vital to my grade that iget this right.
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 21 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer only in the box below.

Question

PLeeeeeeaaaassseeee help, its very vital to my grade that iget this right.
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 21 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer only in the box below.

anonymous · Answer

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

The distance between the  ropes is 40.98 feet

anonymous · Answer

One more
A ladder leans against a house at a 60° angle to the ground. 
If the ladder extends to a length of 166 inches, what is the height of the house rounded to the nearest hundredth of an inch? Type the numeric answer only in the box below.

anonymous · Answer

AND THANK YOU

anonymous · Answer

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anonymous · Answer

wrong one -_-
A toddler's playground has two slides on either side. The slide on the left is situated at a 45° angle to the ground and is 64 centimeters away from the base of the playground. The slide on the right is positioned at a 30° angle to the ground and is 106 centimeters away from the playground's base.
What is the total length of both slides on this playground rounded to the nearest tenth of a centimeter? Type the numeric answer only in the box below.

anonymous · Answer

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anonymous · Answer

on the first one you answered where did the 15 come from

anonymous · Answer

attachment

anonymous · Answer

If 64cm and 106cm away from the base mean vertical length:

sin45° = 64/ L ----> L = 64/ (√2/2) = 90.51 cm
Similarly, 
--> R = 106/ (1/2) = 212cm
Thus, L + R = 302.51cm

If 64cm and 106cm away from the base means horizontal length:
L = 90.51cm
cos30° = 106/ R --> R = 106/ (√3/2) = 212/ √3 = 122.40cm
Thus, L + R = 212.91 cm

anonymous · Answer

there si the pic to go with it, sorry im so confusing

anonymous · Answer

and which number is the total numer of the length of both slides

anonymous · Answer

someone please help, i am very much desperate