Two men, 400 feet apart, observe a balloon between them it is the same vertical plane as they are. the respective angles of elevaation of the balloon are observed by the men to be 75 degrees 20' and 49 degrees30'. find x rounded to the nearest whole number.

The answer is 471 feet.

If A = man to left of balloon 
B = balloon 
C = man to right of balloon 

∠BAC = 75°20' 
∠BCA = 49°30' 
∠ABC = 180 - 75°20' - 49°30' = 55°10' 
AB = 400 ft 

Now we have to find the value of x, which is the side opposite to angle of 75°20' 

Using Law of Sines: 
x/sin(75°20') = 400/sin(55°10') 
x = 400 * sin(75°20') / sin(55°10') 
x = 471.44 
x = 471 ft