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Common Core: 8th Grade Math : Apply the Pythagorean Theorem to Determine Unknown Side Lengths in Right Triangles: CCSS.Math.Content.8.G.B.7

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #441 : Grade 8

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$39\textup{ cm}$

$42\textup{ cm}$

$43\textup{ cm}$

$41\textup{ cm}$

$40\textup{ cm}$

Correct answer:

$40\textup{ cm}$

Explanation:

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle."

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

24^2+32^2=c^2

$576+1\textup,024=c^2$

$1\textup,600=c^2$

$\sqrt{1\textup,600}=\sqrt{c^2}$

Report an Error

Example Question #122 : Geometry

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$78\textup{ cm}$

$77\textup{ cm}$

$75\textup{ cm}$

$79\textup{ cm}$

$76\textup{ cm}$

Correct answer:

$75\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

72^2+21^2=c^2

$5\textup,184+441=c^2$

$5\textup,625=c^2$

$\sqrt{5\textup,625}=\sqrt{c^2}$

75=c

Report an Error

Example Question #33 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$12\textup{ cm}$

$14\textup{ cm}$

$15\textup{ cm}$

$16\textup{ cm}$

$13\textup{ cm}$

Correct answer:

$13\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

12^2+5^2=c^2

144+25=c^2

169=c^2

$\sqrt{169}=\sqrt{c^2}$

13=c

Report an Error

Example Question #34 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$17\textup{ cm}$

$19\textup{ cm}$

$21\textup{ cm}$

$20\textup{ cm}$

$18\textup{ cm}$

Correct answer:

$20\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

16^2+12^2=c^2

256+144=c^2

400=c^2

$\sqrt{400}=\sqrt{c^2}$

20=c

Report an Error

Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$6\textup{ cm}$

$4\textup{ cm}$

$5\textup{ cm}$

$7\textup{ cm}$

$3\textup{ cm}$

Correct answer:

$5\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

4^2+3^2=c^2

16+9=c^2

25=c^2

$\sqrt{25}=\sqrt{c^2}$

5=c

Report an Error

Example Question #36 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$10\textup{ cm}$

$9\textup{ cm}$

$7\textup{ cm}$

$6\textup{ cm}$

$8\textup{ cm}$

Correct answer:

$10\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

8^2+6^2=c^2

64+36=c^2

100=c^2

$\sqrt{100}=\sqrt{c^2}$

10=c

Report an Error

Example Question #37 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$15\textup{ cm}$

$12\textup{ cm}$

$14\textup{ cm}$

$16\textup{ cm}$

$13\textup{ cm}$

Correct answer:

$12\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

10^2+6^2=c^2

100+36=c^2

136=c^2

$\sqrt{136}=\sqrt{c^2}$

11.6=c

c=12

Report an Error

Example Question #38 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$7\textup{ cm}$

$6\textup{ cm}$

$9\textup{ cm}$

$8\textup{ cm}$

$5\textup{ cm}$

Correct answer:

$8\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

7^2+4^2=c^2

49+16=c^2

65=c^2

$\sqrt{65}=\sqrt{c^2}$

8.06=c

c=8

Report an Error

Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$17\textup{ cm}$

$19\textup{ cm}$

$18\textup{ cm}$

$16\textup{ cm}$

$15\textup{ cm}$

Correct answer:

$15\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

9^2+12^2=c^2

81+144=c^2

225=c^2

$\sqrt{225}=\sqrt{c^2}$

15=c

Report an Error

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Common Core: 8th Grade Math : Apply the Pythagorean Theorem to Determine Unknown Side Lengths in Right Triangles: CCSS.Math.Content.8.G.B.7

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #441 : Grade 8

Example Question #122 : Geometry

Example Question #33 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #34 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #36 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #37 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #38 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

All Common Core: 8th Grade Math Resources

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