A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 60 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 80 feet. Please helpppppp!!!!! :(
60^2 + h^2 = 80^2
To find the altitude of the balloon, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the rope, the distance from the stake to the balloon, is the hypotenuse, and the altitude is one of the other sides.
Let's denote the altitude of the balloon as 'h'. The horizontal distance from the stake to the flag pole is 60 feet, and the length of the rope is 80 feet.
Using the Pythagorean theorem, we can write the equation:
(60)^2 + h^2 = (80)^2
Simplifying this equation:
3600 + h^2 = 6400
Subtracting 3600 from both sides:
h^2 = 6400 - 3600
h^2 = 2800
To find the value of 'h,' we need to take the square root of both sides:
β(h^2) = β2800
h β 52.92 feet
Therefore, the altitude of the balloon is approximately 52.92 feet.