Math / Geometry

QuestionAnswer Attempt 1 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

Studdy Solution

STEP 1

1. The triangle is a right triangle with sides $\overline{RQ}$ , $\overline{QS}$ , and hypotenuse $\overline{RS}$ .
2. The length of $\overline{RQ}$ is $5 \, \text{cm}$ .
3. The length of the hypotenuse $\overline{RS}$ is $6.6 \, \text{cm}$ .
4. We need to find the length of $\overline{QS}$ using the Pythagorean Theorem and round the result to three decimal places.

STEP 2

1. Apply the Pythagorean Theorem to find the length of $\overline{QS}$ .
2. Calculate and simplify the expression.
3. Round the result to three decimal places.

STEP 3

Apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse ( $c$ ) is equal to the sum of the squares of the lengths of the other two sides ( $a$ and $b$ ):
$c^2 = a^2 + b^2$
Here, $c = 6.6 \, \text{cm}$ , $a = 5 \, \text{cm}$ , and $b = \overline{QS}$ .
$(6.6)^2 = (5)^2 + (\overline{QS})^2$

STEP 4

Calculate the squares:
$6.6^2 = 43.56$ $5^2 = 25$
Substitute these values into the equation:
$43.56 = 25 + (\overline{QS})^2$

STEP 5

Solve for $(\overline{QS})^2$ :
$(\overline{QS})^2 = 43.56 - 25$ $(\overline{QS})^2 = 18.56$

STEP 6

Take the square root of both sides to find $\overline{QS}$ :
$\overline{QS} = \sqrt{18.56}$

STEP 7

Calculate the square root and round to three decimal places:
$\overline{QS} \approx 4.309$
The actual length of $\overline{QS}$ is:
$\boxed{4.309 \, \text{cm}}$

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QuestionAnswer Attempt 1 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

Studdy Solution

STEP 1

STEP 2

1. Apply the Pythagorean Theorem to find the length of $\overline{QS}$ .
2. Calculate and simplify the expression.
3. Round the result to three decimal places.

STEP 3

STEP 4

Calculate the squares:
$6.6^2 = 43.56$ $5^2 = 25$
Substitute these values into the equation:
$43.56 = 25 + (\overline{QS})^2$

STEP 5

Solve for $(\overline{QS})^2$ :
$(\overline{QS})^2 = 43.56 - 25$ $(\overline{QS})^2 = 18.56$

STEP 6

Take the square root of both sides to find $\overline{QS}$ :
$\overline{QS} = \sqrt{18.56}$

STEP 7

Calculate the square root and round to three decimal places:
$\overline{QS} \approx 4.309$
The actual length of $\overline{QS}$ is:
$\boxed{4.309 \, \text{cm}}$

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QuestionAnswer Attempt 1 out of 2Estimated length of QS‾=4.3 cm\overline{Q S}=4.3 \mathrm{~cm}QS​=4.3 cm The actual length of QS‾=\overline{Q S}=QS​= □\square□ cm (round to 3 decimal places)

Studdy Solution

STEP 1

STEP 2

1. Apply the Pythagorean Theorem to find the length of QS‾ \overline{QS} QS​.2. Calculate and simplify the expression.3. Round the result to three decimal places.

STEP 3

STEP 4

Calculate the squares:6.62=43.56 6.6^2 = 43.56 6.62=43.56 52=25 5^2 = 25 52=25Substitute these values into the equation:43.56=25+(QS‾)2 43.56 = 25 + (\overline{QS})^2 43.56=25+(QS​)2

STEP 5

Solve for (QS‾)2 (\overline{QS})^2 (QS​)2:(QS‾)2=43.56−25 (\overline{QS})^2 = 43.56 - 25 (QS​)2=43.56−25 (QS‾)2=18.56 (\overline{QS})^2 = 18.56 (QS​)2=18.56

STEP 6

Take the square root of both sides to find QS‾ \overline{QS} QS​:QS‾=18.56 \overline{QS} = \sqrt{18.56} QS​=18.56​

STEP 7

Calculate the square root and round to three decimal places:QS‾≈4.309 \overline{QS} \approx 4.309 QS​≈4.309 The actual length of QS‾ \overline{QS} QS​ is:4.309 cm \boxed{4.309 \, \text{cm}} 4.309cm​

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QuestionAnswer Attempt 1 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

1. Apply the Pythagorean Theorem to find the length of $\overline{QS}$ .
2. Calculate and simplify the expression.
3. Round the result to three decimal places.

Calculate the squares:
$6.6^2 = 43.56$ $5^2 = 25$
Substitute these values into the equation:
$43.56 = 25 + (\overline{QS})^2$

Solve for $(\overline{QS})^2$ :
$(\overline{QS})^2 = 43.56 - 25$ $(\overline{QS})^2 = 18.56$

Take the square root of both sides to find $\overline{QS}$ :
$\overline{QS} = \sqrt{18.56}$

Calculate the square root and round to three decimal places:
$\overline{QS} \approx 4.309$
The actual length of $\overline{QS}$ is:
$\boxed{4.309 \, \text{cm}}$