A guy rope is attached to the top of a tent pole. The guy rope is pegged into the ground 7 feet from the tent. If the guy rope is 11 feet long, how long is the tent pole? Round to one decimal place as needed.
assuming the pole is vertical, its height is√(11^2-7^2) ...
To find the length of the tent pole, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the tent pole, the guy rope, and the distance from the tent to the peg form a right triangle. Let's label the length of the tent pole as 'x'.
Using the Pythagorean theorem, we have the equation: x^2 = 11^2 - 7^2
Simplifying the equation, we have: x^2 = 121 - 49
x^2 = 72
To solve for x, we take the square root of both sides: x = √72
Using a calculator, we can find that √72 is approximately 8.5 to one decimal place.
Therefore, the length of the tent pole is approximately 8.5 feet.