Question

Charlie is watching hot air balloons. Balloon A has risen at a 56° angle. Balloon B has risen at an 81° angle. If the distance from balloon A to the ground is 1,200 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number.

Two points labeled Balloon A and Balloon B are connected to a point labeled Charlie, which is on a straight line labeled Ground. A dashed line connects point Balloon A to line Ground; another dashed line connects point Balloon B to line Ground; both dashed lines form a right angle with line Ground; the angle formed from point Balloon A, point Charlie, and line Ground measures x degrees; and the angle formed by point Balloon B, point Charlie, and line Ground measures y degrees.

Answer 1

lets try drawing the scenario

Answer 2

So using trig functions. We can find the x-value distance between Charlie and point A.
So \[\tan(56)=1200/g\]
So \[g=1200/(\tan(56))\]

Answer 3

Similarly \[\tan(81)=1200/f\]
So
\[f=1200/\tan(81)\]

Answer 4

You never told us if b is on the opposite side of A or not
for ex) In that case. Add the values of g and f. If it is like the first situation, then g-f.

Answer 5

btw, x = 56 degrees and y= 81 degrees.