If two legs of a right triangle are 9 and 11, the hypotenuse is
If two legs of a right triangle are 9 and 7, the hypotenuse is
In all cases, if the two legs are a and b, then the hypotenuse c can be found using
c^2 = a^2 + b^2
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's use this theorem to find the length of the hypotenuse:
First, label the two legs of the right triangle as a and b.
In this case, a = 9 and b = 11.
The Pythagorean theorem is: c^2 = a^2 + b^2
where c is the hypotenuse.
Substituting the given values, we have: c^2 = 9^2 + 11^2
Now, calculate the squares of the two given numbers:
9^2 = 81
11^2 = 121
Substitute these values back into the equation: c^2 = 81 + 121
Adding the values on the right side of the equation: c^2 = 202
To find the value of c, we take the square root of both sides:
√(c^2) = √202
Simplifying the equation: c = √202
Therefore, the length of the hypotenuse is approximately √202.
To find the length of the hypotenuse of a right triangle when the lengths of the other two sides, known as the legs, are given, we can use the Pythagorean theorem.
According to the Pythagorean theorem, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
So, in this case, the lengths of the two legs are 9 and 11. Let's label them as a = 9 and b = 11.
The Pythagorean theorem can be written as:
a^2 + b^2 = c^2
where c represents the length of the hypotenuse.
Plugging in the values we have:
9^2 + 11^2 = c^2
81 + 121 = c^2
202 = c^2
To solve for c, we take the square root of both sides:
√202 = √(c^2)
√202 = c
So, the length of the hypotenuse is √202 (approximately 14.21).