Janelle is shooting free throws at a basketball hoop 9 feet off the ground. The hoop forms a 90 degree angle with the ground and she is standing 6 feet away. The diagram below shows a right triangle formed between Jenelle and the basketball hoop. The hypotenuse of a right triangle represents the side opposite the 90 degree angle. The length of that hypotenuse, represented by c can be found using the formula c^2=a^2 +b^2. find the length of the hypotenuse, which represents the shortest distance between jenelle and the hoop, in simplified form.
Using the given information, we can label the sides of the right triangle:
a = 6 feet (distance between Janelle and the hoop on the ground)
b = 9 feet (height of the hoop from the ground)
We can use the Pythagorean theorem to find the length of the hypotenuse (c):
c^2 = a^2 + b^2
c^2 = (6 feet)^2 + (9 feet)^2
c^2 = 36 feet^2 + 81 feet^2
c^2 = 117 feet^2
Taking the square root of both sides to find c, the length of the hypotenuse:
c = √(117 feet^2)
c = √(9 * 13 feet^2)
c = √(9) * √(13) * feet
c = 3 * √(13) * feet
Therefore, the length of the hypotenuse (shortest distance between Janelle and the hoop) is 3√(13) feet.
To find the length of the hypotenuse, which represents the shortest distance between Janelle and the hoop, we can use the Pythagorean theorem.
According to the given information, the side adjacent to the 90-degree angle (the height of the hoop) is 9 feet, and the side opposite to the 90-degree angle (the distance between Janelle and the hoop) is 6 feet.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse, a is the length of the side adjacent to the 90-degree angle, and b is the length of the side opposite the 90-degree angle.
Plugging in the values we have:
c^2 = 6^2 + 9^2
Simplifying the equation:
c^2 = 36 + 81
c^2 = 117
To find the length of the hypotenuse, we take the square root of both sides:
c = √117
The length of the hypotenuse, representing the shortest distance between Janelle and the hoop, in simplified form, is √117.
To find the length of the hypotenuse (c), we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we know the lengths of the other two sides:
a = 6 feet (the horizontal distance between Janelle and the hoop)
b = 9 feet (the height of the hoop above the ground)
Now, we can substitute these values into the Pythagorean theorem formula:
c^2 = a^2 + b^2
Substituting the values:
c^2 = 6^2 + 9^2
c^2 = 36 + 81
c^2 = 117
To find the length of the hypotenuse (c), we need to take the square root of both sides:
√(c^2) = √(117)
c = √(117)
The length of the hypotenuse, representing the shortest distance between Janelle and the hoop, in simplified form is √117.