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.

Because x is not defined, it is assumed to be the height of the balloon.

Note that
75° 20' = 75.333°
49° 30' = 49.5°

From the figure shown below, obtain by definition,
a = x cot 49.5° = 0.8541x
b = x cot 75.333° = 0.2617x

Because a + b = 400 ft, therefore
0.8541x + 0.2617x = 400
1.1158x = 400
x = 358.49 ft

358 ft (nearest whole number)