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Basic Geometry : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #21 : Right Triangles

Find the length of the missing side.

Possible Answers:

24.21

23.64

19.58

22.91

Correct answer:

22.91

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-10^2}=\sqrt{525}=22.91$

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Example Question #1201 : Basic Geometry

Find the length of the missing side.

Possible Answers:

25.91

21.93

19.33

24.36

Correct answer:

21.93

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-12^2}=\sqrt{481}=21.93$

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Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

12.36

19.55

Correct answer:

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-15^2}=\sqrt{400}=20$

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Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

17.75

18.25

19.39

16.81

Correct answer:

17.75

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-3^2}=\sqrt{315}=17.75$

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Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

21.57

17.98

13.69

16.58

Correct answer:

16.58

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-7^2}=\sqrt{275}=16.58$

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Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

16.23

14.52

15.59

17.99

Correct answer:

15.59

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-9^2}=\sqrt{243}=15.59$

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Example Question #14 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

14.62

16.97

18.92

12.68

Correct answer:

16.97

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-6^2}=\sqrt{288}=16.97$

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Example Question #15 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

Correct answer:

Explanation:

Recall the Pythagorean Theorem for a right triangle:

a^2+b^2=c^2

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

b^2=c^2-a^2

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{17^2-8^2}=\sqrt{225}=15$

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Example Question #16 : How To Find The Length Of The Side Of A Right Triangle

Tri 3

Given the right triangle above, find the value of .

Possible Answers:

Correct answer:

Explanation:

To find the length of the side x, we must use the Pythagorean Theorem

a^2+b^2=c^2 .

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

4^2+b^2=5^2

which can be simplified to

16+b^2=25 .

Next, solve for b and we get a final answer of

$b=\sqrt{9}=3$ .

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.

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Example Question #14 : How To Find The Length Of The Side Of A Right Triangle

Tri 5

Given the right triangle above, find the length of the missing side.

Possible Answers:

Correct answer:

Explanation:

To find the length of the side x, we must use the Pythagorean Theorem

a^2+b^2=c^2 .

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

9^2+b^2=41^2

which can be simplified to

81+b^2=1681 .

Next, solve for b and we get a final answer of

$b=\sqrt{1600}=40$ .

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.

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Basic Geometry : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #21 : Right Triangles

Example Question #1201 : Basic Geometry

Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

Example Question #14 : How To Find The Length Of The Side Of A Right Triangle

Example Question #15 : How To Find The Length Of The Side Of A Right Triangle

Example Question #16 : How To Find The Length Of The Side Of A Right Triangle

Example Question #14 : How To Find The Length Of The Side Of A Right Triangle

All Basic Geometry Resources

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