A helium-filled balloon is attached to a 120 m long string. The string is tied to a hook on the ground and it makes an angle of 30° with the ground, as shown below.
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0408_16/image0024e2f1677.jpg
What is the height of the balloon from the ground?
Options are:
60m
84.84m
120m
103.92m
I am obviously doing something wrong when I work the problem because I keep coming up with the answer of 169.70.
Can someone tell me what I am doing wrong and help!?!?!

Question

A helium-filled balloon is attached to a 120 m long string. The string is tied to a hook on the ground and it makes an angle of 30° with the ground, as shown below. 
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0408_16/image0024e2f1677.jpg
What is the height of the balloon from the ground?
Options are:
60m
84.84m
120m
103.92m
I am obviously doing something wrong when I work the problem because I keep coming up with the answer of 169.70. 
Can someone tell me what I am doing wrong and help!?!?!

anonymous · Answer

In a 30-60-90 triangle, the longest side (in this case, the string) is always twice as much as the shortest side (in this case the height).  You know the height is the shortest side because it's across from the 30 degree angle.

btaylor · Answer

|dw:1339703381223:dw|
sin 30 = h/120 --> h=120 sin 30
h = 120 x 0.5
h = 60m
I don't know how you are getting 169.70. That is 100% impossible