A guy rope is attached to the top of a tent pole. The tent pole is 8 feet tall. If the guy rope is pegged into the ground 5 feet from the tent, how long is the guy rope?
you just have a right triangle with legs 5 and 8. So, the rope, forming the hypotenuse is
√(25+64) = √89
you just have a right triangle with legs 5 and 8. So, the rope, forming the hypotenuse is
√(25+64) = √89
To find the length of the guy rope, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the guy rope) is equal to the sum of the squares of the other two sides.
In this case, the tent pole forms one side of the right triangle, and the distance from the peg to the tent forms the other side. The guy rope, being attached to the top of the tent pole, is the hypotenuse.
Let's label the length of the guy rope as 'c', the height of the tent pole as 'a', and the distance from the peg to the tent as 'b'.
Using the Pythagorean theorem, the equation becomes:
c² = a² + b²
Plugging in the given values:
a = 8 feet (height of the tent pole)
b = 5 feet (distance from the peg to the tent)
we get:
c² = 8² + 5²
c² = 64 + 25
c² = 89
To find c, we take the square root of both sides:
c = √89
This gives us the length of the guy rope, which is approximately 9.4 feet.
To find the length of the guy rope, we can use the Pythagorean theorem. This theorem states that in a right 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 tent pole can be considered as the vertical side of the right triangle, and the distance from the tent to the peg in the ground is the horizontal side. The guy rope is the hypotenuse.
So, let's apply the Pythagorean theorem:
Length of guy rope^2 = Length of tent pole^2 + Distance from tent to the peg^2
Plugging in the values, we have:
Length of guy rope^2 = 8^2 + 5^2
Simplifying, we get:
Length of guy rope^2 = 64 + 25
Length of guy rope^2 = 89
To find the length of the guy rope, we need to take the square root of both sides:
Length of guy rope = √89
Using a calculator, we find that the length of the guy rope is approximately 9.43 feet.