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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 #62 : Plane Geometry

The legs of a right triangle are equal to 4 and 5. What is the length of the hypotenuse?

Possible Answers:

$\sqrt{41}$

Correct answer:

$\sqrt{41}$

Explanation:

If the legs of a right triangle are 4 and 5, to find the hypotenuse, the following equation must be used to find the hypotenuse, in which c is equal to the hypotenuse:

$a^2{+b^{2}}=c^2$

$4^2{+5^{2}}=c^2$

16+25=c^2

$41=c^{2}$

$c={\sqrt{41}}$

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Example Question #53 : Triangles

Righttriangle

Triangle ABC is a right triangle. If the length of side A = 3 inches and C = 5 inches, what is the length of side B?

Possible Answers:

6 inches

1 inches

1/2 inches

4.5 inches

4 inches

Correct answer:

4 inches

Explanation:

Using the Pythagorean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This gives:

$3^{2} + b^{2} = 5^{2}$

$9 + b^{2} = 25$

Subtracting 9 from both sides of the equation gives:

$b^{2} = 16$

b = 4 inches

Righttriangle

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Example Question #82 : Geometry

An 8-foot-tall tree is perpendicular to the ground and casts a 6-foot shadow. What is the distance, to the nearest foot, from the top of the tree to the end of the shadow?

Possible Answers:

$\dpi{100} \small 4$

$\dpi{100} \small 6$

$\dpi{100} \small 5$

$\dpi{100} \small 10$

$\dpi{100} \small 8$

Correct answer:

$\dpi{100} \small 10$

Explanation:

In order to find the distance from the top of the tree to the end of the shadow, draw a right triangle with the height(tree) labeled as 8 and base(shadow) labeled as 6:

Screen_shot_2013-08-16_at_12.34.40_am

From this diagram, you can see that the distance being asked for is the hypotenuse. From here, you can either use the Pythagorean Theorem:

$\dpi{100} \small a^{2}+b^{2}=c^{2}$

or you can notice that this is simililar to a 3-4-5 triangle. Since the lengths are just increased by a factor of 2, the hypotenuse that is normally 5 would be 10.

8^2+6^2=c^2

64+36=c^2

100=c^2

10=c

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Example Question #62 : Triangles

Find the perimeter of the polygon.

Possible Answers:

Correct answer:

Explanation:

Divide the shape into a rectangle and a right triangle as indicated below.

Find the hypotenuse of the right triangle with the Pythagorean Theorem, a^2 + b^2 = c^2 , where and are the legs of the triangle and is its hypotenuse.

(8)^2+(6)^2 = c^2

100 = c^2

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

c =10

This is our missing length.

Now add the sides of the polygon together to find the perimeter:

20 + 10 + 26 + 8 = 64

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Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

Correct answer:

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{12^2 + 16^2}=\sqrt{400}=20$

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Example Question #11 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$2\sqrt{113}$

$6\sqrt{13}$

256

$2\sqrt{111}$

Correct answer:

$2\sqrt{113}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{14^2 + 16^2}=\sqrt{452}=2\sqrt{113}$

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Example Question #284 : Triangles

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$3\sqrt5$

$\sqrt5$

$4\sqrt5$

$2\sqrt5$

Correct answer:

$2\sqrt5$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{2^2 + 4^2}=\sqrt{20}=2\sqrt5$

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Example Question #12 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$5\sqrt5$

$4\sqrt5$

$2\sqrt{10}$

$6\sqrt5$

Correct answer:

$5\sqrt5$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{5^2 + 10^2}=\sqrt{125}=5\sqrt5$

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Example Question #425 : Grade 8

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$3\sqrt3$

$\sqrt{26}$

$2\sqrt6$

Correct answer:

$\sqrt{26}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{1^2 + 5^2}=\sqrt{26}$

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Example Question #431 : Grade 8

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$2\sqrt{41}$

$3\sqrt{41}$

$\sqrt{41}$

$4\sqrt{41}$

Correct answer:

$3\sqrt{41}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{15^2 + 12^2}=\sqrt{369}=3\sqrt{41}$

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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 #62 : Plane Geometry

Example Question #53 : Triangles

Example Question #82 : Geometry

Example Question #62 : Triangles

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #11 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #284 : Triangles

Example Question #12 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #425 : Grade 8

Example Question #431 : Grade 8

All Common Core: 8th Grade Math Resources

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