Question

Charlie is watching hot air balloons. Balloon A has risen at a 60° angle. Balloon B has risen at an 82° angle. If the distance from balloon A to the ground is 1,400 feet, how far is balloon B from balloon A?

Answer 1

The distance between Balloon B and Balloon A is approximately 8,189.6ft.

Step-by-step explanation:

To find the distance between Balloon A and Balloon B, we can use trigonometry.

We know that the distance from Balloon A to the ground is 1,400 feet and the angle of ascent is 60 degrees. We can use the sine function to find the height of Balloon A above the ground:

sin(60) = height / 1,400ft

height = 1,400ft * sin(60)

height = 1,400ft * 0.866 (rounded to three decimal places)

height ≈ 1,212.4ft

Now, to find the distance between Balloon A and Balloon B, we can use the tangent function:

tan(82) = distance between Balloon A and Balloon B / height of Balloon A above the ground

distance between Balloon A and Balloon B = height of Balloon A above the ground * tan(82)

distance between Balloon A and Balloon B ≈ 1,212.4ft * 6.747 (rounded to three decimal places)

distance between Balloon A and Balloon B ≈ 8,189.6ft