QuestionFind $b$ in the Pythagorean theorem $3^2 + b^2 = 5^2$ . Round your answer to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The Pythagorean theorem is given by a^ + b^ = c^ . The value of $a$ is33. The value of $c$ is54. We need to find the value of $b$
5. If $b$ is an irrational number, we need to round it to two decimal places

STEP 2

First, we need to rearrange the Pythagorean theorem to solve for $b$ . $b^2 = c^2 - a^2$

STEP 3

Now, plug in the given values for $a$ and $c$ to calculate $b^2$ .
$b^2 =5^2 -3^2$

STEP 4

Calculate the value of $b^2$ .
$b^2 =25 -9 =16$

STEP 5

Now that we have the value of $b^2$ , we can find the value of $b$ by taking the square root of $b^2$ .
$b = \sqrt{b^2}$

STEP 6

Plug in the value for $b^2$ to calculate $b$ .
$b = \sqrt{16}$

STEP 7

Calculate the value of $b$ .
$b = \sqrt{16} =4$ Therefore, the value of $b$ is4.

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QuestionFind $b$ in the Pythagorean theorem $3^2 + b^2 = 5^2$ . Round your answer to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The Pythagorean theorem is given by a^ + b^ = c^ . The value of $a$ is33. The value of $c$ is54. We need to find the value of $b$
5. If $b$ is an irrational number, we need to round it to two decimal places

STEP 2

First, we need to rearrange the Pythagorean theorem to solve for $b$ . $b^2 = c^2 - a^2$

STEP 3

Now, plug in the given values for $a$ and $c$ to calculate $b^2$ .
$b^2 =5^2 -3^2$

STEP 4

Calculate the value of $b^2$ .
$b^2 =25 -9 =16$

STEP 5

Now that we have the value of $b^2$ , we can find the value of $b$ by taking the square root of $b^2$ .
$b = \sqrt{b^2}$

STEP 6

Plug in the value for $b^2$ to calculate $b$ .
$b = \sqrt{16}$

STEP 7

Calculate the value of $b$ .
$b = \sqrt{16} =4$ Therefore, the value of $b$ is4.

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QuestionFind bbb in the Pythagorean theorem 32+b2=523^2 + b^2 = 5^232+b2=52. Round your answer to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The Pythagorean theorem is given by a^ + b^ = c^ . The value of aaa is33. The value of ccc is54. We need to find the value of bbb5. If bbb is an irrational number, we need to round it to two decimal places

STEP 2

First, we need to rearrange the Pythagorean theorem to solve for bbb.b2=c2−a2b^2 = c^2 - a^2b2=c2−a2

STEP 3

Now, plug in the given values for aaa and ccc to calculate b2b^2b2.b2=52−32b^2 =5^2 -3^2b2=52−32

STEP 4

Calculate the value of b2b^2b2.b2=25−9=16b^2 =25 -9 =16b2=25−9=16

STEP 5

Now that we have the value of b2b^2b2, we can find the value of bbb by taking the square root of b2b^2b2.b=b2b = \sqrt{b^2}b=b2​

STEP 6

Plug in the value for b2b^2b2 to calculate bbb.b=16b = \sqrt{16}b=16​

STEP 7

Calculate the value of bbb.b=16=4b = \sqrt{16} =4b=16​=4Therefore, the value of bbb is4.

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

QuestionFind $b$ in the Pythagorean theorem $3^2 + b^2 = 5^2$ . Round your answer to two decimal places.

Assumptions1. The Pythagorean theorem is given by a^ + b^ = c^ . The value of $a$ is33. The value of $c$ is54. We need to find the value of $b$
5. If $b$ is an irrational number, we need to round it to two decimal places

First, we need to rearrange the Pythagorean theorem to solve for $b$ . $b^2 = c^2 - a^2$

Now, plug in the given values for $a$ and $c$ to calculate $b^2$ .
$b^2 =5^2 -3^2$

Calculate the value of $b^2$ .
$b^2 =25 -9 =16$

Now that we have the value of $b^2$ , we can find the value of $b$ by taking the square root of $b^2$ .
$b = \sqrt{b^2}$

Plug in the value for $b^2$ to calculate $b$ .
$b = \sqrt{16}$

Calculate the value of $b$ .
$b = \sqrt{16} =4$ Therefore, the value of $b$ is4.