The balloon is 118 feet high.
Imagine two wires, each 140 ft long, tethered to a balloon in the sky. The wires are attached to the ground, 75 ft apart. We want to find the height of the balloon above the ground.
To do this, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the length of the wire, which is 140 ft. The other two sides are the height of the balloon above the ground and the horizontal distance between the two wires, which is 75 ft.
So, we can draw a right triangle with the following dimensions:
hypotenuse = 140 ft
side 1 = height of balloon
side 2 = 75 ft
We can then use the Pythagorean theorem to set up the following equation:
hypotenuse^2 = side 1^2 + side 2^2
140^2 = height of balloon^2 + 75^2
Solving for the height of the balloon, we get:
height of balloon = sqrt(140^2 - 75^2)
height of balloon = sqrt(19600 - 5625)
height of balloon = sqrt(13975)
height of balloon = 118.3 ft
Rounding to the nearest whole number, the height of the balloon above the ground is 118 ft.