Ahot air balloon is flying above groveburg. to the left side of the balloon, the balloonist measure the angle of depression to the groveburg soccer fields to be 649-10-01-00-00_files/i0210000.jpg 15’. to the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 649-10-01-00-00_files/i0210001.jpg 30’. the distance between the two athletic complexes is 4 miles.

The complete question: 
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depression to the Groveburg soccer fields to be 20°15’. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62°30’. The distance between the two athletic complexes is 4 miles.
a. Find the distance from the balloon to the soccer fields.
b. Find the distance from the balloon to the football field.

Check all the procedures in the attached picture.

a. The first thing we are going to do is convert 15' to degrees. To do that, we are going to take advantage of the fact that 1'=1/60°:
15'*1/60°=0.25°
Now we can express our angle using degrees only: 20°15'=20°+0.25°=20.25°
Now that we have our elevation angle we can use the law of sines to find the distance, , from the balloon to the soccer fields:



miles

We can conclude that the distance from the balloon to the soccer fields is 3.6 miles.

b. Just like before, the first thing we are going to do is convert 30' to degrees:
30'*1/60°=0.5°
Now we can express our angle using degrees only 62°30'=62°+0.5°=62.5°
Lets use the law of sines to find the distance, , from the balloon to the football field:



miles

We can conclude that the distance from the balloon to the football field is 1.4 miles.