From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. if the distance between the radio antenna and the library is 1.3 miles, how many miles high is the balloon?

I will try my best to answer this, but it will be difficult to determine which angles and distances are where since you did not provide the picture. 

You can use the tangent of the 57 degree angle to find your answer. 
tan=opposite/adjacent 
tan(57 degrees)=1.3/X
X=1.3/tan(57 degrees)