Charlie is watching hot air balloons. Balloon A has risen at a 50° angle. Balloon B has risen at a 78° angle. If the distance from balloon A to the ground is 1,000 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number.

999 feet
1,005 feet
1,052 feet
1,102 feet

The answer to your question is 1052 ft

Step-by-step explanation:

Data

∠A = 50°

∠B = 78°

Distance from A to the ground = 1000 ft

Process

1.- To solve this problem use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.

              tan Ф = Opposite side / adjacent side

-Solve for adjacent side

               Adjacent side = Opposite side / tan Ф

-For the left triangle

              Adjacent side = 1000 / tan 50

-Simplification

              Adjacent side = 839.1 ft

2.- Calculate the adjacent side of the right triangle

              Adjacent side = 1000/ tan 78

-Simplification

             Adjacent side = 1000 / 4.7

-Result

             Adjacent side = 212.56

3.- Distance from A to B

Distance = 839.1 + 212.56

              = 1051.7 ft ≈ 1052 ft

Balloon B is 3910 feet above balloon A.

Step by step explanation:

The figure for the given scenario is shown below.

From the figure,

QR is the distance of balloon A or B from Charlie, SR is the distance of balloon A from ground,  is the angle of elevation of balloon A,  is the angle of elevation of balloon B. S is the position of balloon A and P is the position of balloon B.

So, as per the question,

SR = 1200 ft, °, °.

From triangle ΔSQR,

Now, consider triangle ΔPQR.

Now, difference in the height of balloon A and B is given by the segment PS.

So, Therefore, the balloon B is 3910 feet above balloon A.