Math

QuestionFind xx in a right triangle with sides 10 and 11 using the Pythagorean theorem.

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. The lengths of the other two sides are10 and113. We are using the Pythagorean theorem to find the length of xx

STEP 2

The Pythagorean 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 lengths of the other two sides. We can write this asc2=a2+b2c^2 = a^2 + b^2where cc is the length of the hypotenuse, and aa and bb are the lengths of the other two sides.

STEP 3

In this problem, we are trying to find the length of xx, which is the hypotenuse of the triangle. So, we can rewrite the Pythagorean theorem asx2=a2+b2x^2 = a^2 + b^2

STEP 4

Now, plug in the given values for aa and bb to calculate x2x^2.
x2=102+112x^2 =10^2 +11^2

STEP 5

Calculate the value of x2x^2.
x2=100+121=221x^2 =100 +121 =221

STEP 6

To find the length of xx, we need to take the square root of x2x^2.
x=x2x = \sqrt{x^2}

STEP 7

Plug in the value for x2x^2 to calculate xx.
x=221x = \sqrt{221}

STEP 8

Calculate the length of xx.
x=22114.87x = \sqrt{221} \approx14.87The length of xx is approximately14.87.

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