QuestionFind the side length $b$ using $a=5$ and $c=6$ . Rationalize denominators when needed. Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. We are given a triangle with sides a, b, and c. . The lengths of sides a and c are given as5 and6 respectively.
3. We are asked to find the length of side b.
4. We assume that this is a right triangle, and we will use the Pythagorean theorem to find the length of side b.

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. This can be written as $c^2 = a^2 + b^2$

STEP 3

We are given the values for a and c, and we are asked to find b. So, we rearrange the Pythagorean theorem to solve for b $b^2 = c^2 - a^2$

STEP 4

Now, we substitute the given values for a and c into the equation $b^2 =6^2 -^2$

STEP 5

implify the equation $b^2 =36 -25$

STEP 6

Calculate the value of b squared $b^2 =11$

STEP 7

To find the value of b, we take the square root of both sides of the equation $b = \sqrt{11}$ So, the length of side b is $\sqrt{11}$ .

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QuestionFind the side length $b$ using $a=5$ and $c=6$ . Rationalize denominators when needed. Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. We are given a triangle with sides a, b, and c. . The lengths of sides a and c are given as5 and6 respectively.
3. We are asked to find the length of side b.
4. We assume that this is a right triangle, and we will use the Pythagorean theorem to find the length of side b.

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. This can be written as $c^2 = a^2 + b^2$

STEP 3

We are given the values for a and c, and we are asked to find b. So, we rearrange the Pythagorean theorem to solve for b $b^2 = c^2 - a^2$

STEP 4

Now, we substitute the given values for a and c into the equation $b^2 =6^2 -^2$

STEP 5

implify the equation $b^2 =36 -25$

STEP 6

Calculate the value of b squared $b^2 =11$

STEP 7

To find the value of b, we take the square root of both sides of the equation $b = \sqrt{11}$ So, the length of side b is $\sqrt{11}$ .

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QuestionFind the side length bbb using a=5a=5a=5 and c=6c=6c=6. Rationalize denominators when needed. Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. We are given a triangle with sides a, b, and c. . The lengths of sides a and c are given as5 and6 respectively.3. We are asked to find the length of side b.4. We assume that this is a right triangle, and we will use the Pythagorean theorem to find the length of side b.

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. This can be written asc2=a2+b2c^2 = a^2 + b^2c2=a2+b2

STEP 3

We are given the values for a and c, and we are asked to find b. So, we rearrange the Pythagorean theorem to solve for bb2=c2−a2b^2 = c^2 - a^2b2=c2−a2

STEP 4

Now, we substitute the given values for a and c into the equationb2=62−2b^2 =6^2 -^2b2=62−2

STEP 5

implify the equationb2=36−25b^2 =36 -25b2=36−25

STEP 6

Calculate the value of b squaredb2=11b^2 =11b2=11

STEP 7

To find the value of b, we take the square root of both sides of the equationb=11b = \sqrt{11}b=11​So, the length of side b is 11\sqrt{11}11​.

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

QuestionFind the side length $b$ using $a=5$ and $c=6$ . Rationalize denominators when needed. Simplify your answer.

Assumptions1. We are given a triangle with sides a, b, and c. . The lengths of sides a and c are given as5 and6 respectively.
3. We are asked to find the length of side b.
4. We assume that this is a right triangle, and we will use the Pythagorean theorem to find the length of side b.

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. This can be written as $c^2 = a^2 + b^2$

We are given the values for a and c, and we are asked to find b. So, we rearrange the Pythagorean theorem to solve for b $b^2 = c^2 - a^2$

Now, we substitute the given values for a and c into the equation $b^2 =6^2 -^2$

implify the equation $b^2 =36 -25$

Calculate the value of b squared $b^2 =11$

To find the value of b, we take the square root of both sides of the equation $b = \sqrt{11}$ So, the length of side b is $\sqrt{11}$ .