Q:

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.What is the distance from the balloon to the football field?

Accepted Solution

A:
Answer:Solution : 3.6 milesStep-by-step explanation:The first step in solving this problem is to convert 15' to degrees --- (1) . 15' is represented as 15 minutes, so to convert to degrees we have 15 / 60 = 0.25°. Adding 20 + 15' we should get 20 + 0.25 = 20.25 (degrees). Now remember that on the right side we have the football field, 62° 30'. Let's convert that 30' into degrees --- (2). 30 / 60 = 0.5, and 62 + 0.5 = 62.5. Using both this information we can calculate the angle from the balloon to the horizontal. That would be 180 - 20.25 - 62.5 = 97.25°. Therefore the distance from the balloon to the soccer fields would be as follows,distance / sin(62.5) = 4 / sin(97.25)Let distance = x ...x / sin(62.5) = 4 / sin(97.25),x / 0.88701083317 = 4 / 0.99200494968,x * 0.99200494968 = 4 * 0.88701083317,x * 0.99200494968 = 3.548,x = ( About ) 3.5766 milesGiven the options the distance from the balloon to the soccer fields would be 3.6 miles.