Question

Find the length of the leg x. Enter the exact value, not a decimal approximation.
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Answer 1

Answer:

The answer to your question is: x = √ 133

Step-by-step explanation:

This is a right triangle, so let's use the pythagorean theorem,

                        c²  =  a²   +   b²

c = 13

a = 6

b = ?

Substitution

                     13² = 6² + b²

                     169 = 36 + b²

                     b² = 169 - 36

                     b² = 133

                     b = √133 = x

Answer 2

Remember that whenever you have to find remaining side of a right angled triangle, you can use Pythagoras theorem.

For given triangle, the value of x is given as: $x = \sqrt{133} \approx 11.53 \: \rm units$

Given that:

• The right angled triangle has hypotenuse of 13 units

• Its one other side measures 6 units.

• The length of unknown side is denoted by length x units.

To find:

Value of x

Evaluation:

The Pythagoras theorem states that:

"In a right angled triangle, the square of length of its hypotenuse is equal to sum of square of other two sides' lengths"

In a right angled triangle, one of its angle is right angle which means that it has measure of 90 degrees. The slant side is called hypotenuse.

Using Pythagoras theorem for given right triangle we have:

$13^2 = x^2 + 6^2\\169 = x^2 + 36\\x^2 = 169 - 36 = 133\\x = \sqrt{133} \text{\: (Positive root is taken since x denotes length which is non negative quantity)}$

Thus, for given right triangle, the value of x is given as: $x = \sqrt{133} \approx 11.53 \: \rm units$

Learn more about Pythagoras theorem and right angled triangles here:

https://brainly.com/question/396866