Two men, 400 feet apart, observe a balloon between them; it is in the same vertical plane as they are. the respective angles of elevation of the balloon are observed by the men to be 75°20' and 49°30'. find x rounded to the nearest whole number. 318 ft 339 ft 471 ft 504 ft

x = 471 ft

Step-by-step explanation:

Assuming A to be the man to the left of balloon, B to be the balloon and C to be the man to the right of balloon, we can write:

∠BAC = 75°20'  

∠BCA = 49°30'

∠ABC = 180 - 75°20' - 49°30' = 55°10'  

AB = 400 ft

So basically we need to find the value of x, which is the opposite side to the angle of 75°20' using the law of sine:

x/sin(75°20') = 400/sin(55°10')  

x = 400 * sin(75°20') / sin(55°10')  

x = 471.44  

x = 471 ft