A large tent has an adjustable center pole. A rope 26 ft long connects the top of the pole to a peg 24 ft from the bottom of the pole. What is the height of the pole? Round to the nearest hundredth if necessary.
Height of the pole = 22.67 ft
To find the height of the pole, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the rope connecting the top of the pole to the peg forms the hypotenuse of a right triangle, with the pole itself forming one of the other sides.
Let's say the height of the pole is 'h.' According to the problem, the length of the rope is 26 ft and the distance from the peg to the bottom of the pole is 24 ft.
Using the Pythagorean theorem, we can write the equation as follows:
h^2 + 24^2 = 26^2
Simplifying the equation:
h^2 + 576 = 676
Subtracting 576 from both sides:
h^2 = 100
Taking the square root of both sides:
h = √100
Since the square root of 100 is 10, the height of the pole is 10 ft.