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.

I guess x is the height of the balloon. If so

let A be the man on the right & B the one on the left

Let C be the balloon with x its height. The height x intercepts AB in H

At last let AH = y & HB = 400-y

tan (75°20') = x/y = = = > 3.821 = x/y = = > 1) x = 3.821. y

& tan (49°30') = x / (400-y) = = > 1.171 = x / (400-y) = = >2) x=468.4 - 1.171y

but1) = 2) then: 3.821. y = 468.4 - 1.171y==> y = 93.83

Now that y is know, we can calculate CH, that is x

tan (75°20') = x/y = = > 3.82=x/93.83===> x = 358.5 ft