Question

I have one EXTRA hard Geometry question if someone can help!!thnx :)

Answer 1

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 18 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.

Answer 2

And don't we all love EXTRA hard Geometry questions? :)

Answer 3

lol not me!!!

Answer 4

I guess the key here is not to be distracted. Let's redraw, but again, only drawing things that ACTUALLY matter.

Answer 5

Clearly another 30-60-90 triangle, no?

Answer 6

yes!! it is 30-60-90 triangle

Answer 7

Well, refer to the diagram from last time... this time, we're given the side opposite the 30-degree angle.

Answer 8

okay! so same thing but different side??

Answer 9

So... if we're given the length x of the side opposite the 30-degree angle, for instance, the length of the hypotenuse is just 2x, right?

Answer 10

yes!

Answer 11

And what's the other side?

Answer 12

umm..well it would be 18...right??

Answer 13

18, the side opposite the 30-degree angle
36, the hypotenuse

What about the other side?

Answer 14

http://openstudy.com/study#/updates/5138a185e4b01c4790d080c6
refer to the drawing I made of general 30-60-90 triangles.

Answer 15

its x??...sry if I am wrong these things confuse me!! atleast I am trying to learn but I think it is x

Answer 16

Okay, given a 30-60-90 triangle and the side opposite the 30-degree angle

Answer 17

then the hypotenuse is always given by

Answer 18

okay...

Answer 19

And the other side, the one opposite the 60-degree angle is