QuestionFind the hypotenuse of a right triangle with legs 5 and 12. Options: a. 8, b. 169, c. 13, d. 17.

Studdy Solution

STEP 1

Assumptions1. The two legs of the right triangle are5 and12. . The triangle is a right triangle, meaning one of its angles is90 degrees.
3. We are asked to find the length of the hypotenuse.
4. We will use the Pythagorean theorem to solve this problem, which 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.

STEP 2

Let's denote the lengths of the two legs as a and b, and the length of the hypotenuse as c. According to the Pythagorean theorem, we have $c^2 = a^2 + b^2$

STEP 3

Now, plug in the given values for a and b to calculate the hypotenuse.
$c^2 =5^2 +12^2$

STEP 4

Calculate the squares of and12.
$c^2 =25 +144$

STEP 5

Add25 and144 to get the square of the hypotenuse.
$c^2 =169$

STEP 6

To find the length of the hypotenuse, we need to take the square root of169.
$c = \sqrt{169}$

STEP 7

Calculate the square root of169.
$c =13$ The hypotenuse of the right triangle is13.

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QuestionFind the hypotenuse of a right triangle with legs 5 and 12. Options: a. 8, b. 169, c. 13, d. 17.

Studdy Solution

STEP 1

STEP 2

Let's denote the lengths of the two legs as a and b, and the length of the hypotenuse as c. According to the Pythagorean theorem, we have $c^2 = a^2 + b^2$

STEP 3

Now, plug in the given values for a and b to calculate the hypotenuse.
$c^2 =5^2 +12^2$

STEP 4

Calculate the squares of and12.
$c^2 =25 +144$

STEP 5

Add25 and144 to get the square of the hypotenuse.
$c^2 =169$

STEP 6

To find the length of the hypotenuse, we need to take the square root of169.
$c = \sqrt{169}$

STEP 7

Calculate the square root of169.
$c =13$ The hypotenuse of the right triangle is13.

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QuestionFind the hypotenuse of a right triangle with legs 5 and 12. Options: a. 8, b. 169, c. 13, d. 17.

Studdy Solution

STEP 1

STEP 2

Let's denote the lengths of the two legs as a and b, and the length of the hypotenuse as c. According to the Pythagorean theorem, we havec2=a2+b2c^2 = a^2 + b^2c2=a2+b2

STEP 3

Now, plug in the given values for a and b to calculate the hypotenuse.c2=52+122c^2 =5^2 +12^2c2=52+122

STEP 4

Calculate the squares of and12.c2=25+144c^2 =25 +144c2=25+144

STEP 5

Add25 and144 to get the square of the hypotenuse.c2=169c^2 =169c2=169

STEP 6

To find the length of the hypotenuse, we need to take the square root of169.c=169c = \sqrt{169}c=169​

STEP 7

Calculate the square root of169.c=13c =13c=13The hypotenuse of the right triangle is13.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Let's denote the lengths of the two legs as a and b, and the length of the hypotenuse as c. According to the Pythagorean theorem, we have $c^2 = a^2 + b^2$

Now, plug in the given values for a and b to calculate the hypotenuse.
$c^2 =5^2 +12^2$

Calculate the squares of and12.
$c^2 =25 +144$

Add25 and144 to get the square of the hypotenuse.
$c^2 =169$

To find the length of the hypotenuse, we need to take the square root of169.
$c = \sqrt{169}$

Calculate the square root of169.
$c =13$ The hypotenuse of the right triangle is13.