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 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

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 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

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/0404/0404_G6_Q1.gif

anonymous · Answer

@dumbcow

dumbcow · Answer

since you know the height of the balloon is 15, you don't need to worry about Rope 1 it is extra info.
just look at triangle formed by Rope 2 and balloon
it is a right triangle with angles of 30:60:90 this is a special right triangle and the side length ratios are 1:sqrt3:2
15 is opposite the 30 degree angle....so that means hypotenuse is 30 and other side must be 15*sqrt3
|dw:1343276428106:dw|
hope that helps