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

Example Question #211 : Triangles

Find the length of the missing side.

5

Possible Answers:

\displaystyle 22.91

\displaystyle 23.64

\displaystyle 19.58

\displaystyle 24.21

Correct answer:

\displaystyle 22.91

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

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

Find the length of the missing side.

6

Possible Answers:

\displaystyle 19.33

\displaystyle 24.36

\displaystyle 21.93

\displaystyle 25.91

Correct answer:

\displaystyle 21.93

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

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

Find the length of the missing side.

7

Possible Answers:

\displaystyle 12.36

\displaystyle 17

\displaystyle 20

\displaystyle 19.55

Correct answer:

\displaystyle 20

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

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

Find the length of the missing side.

8

Possible Answers:

\displaystyle 16.81

\displaystyle 19.39

\displaystyle 17.75

\displaystyle 18.25

Correct answer:

\displaystyle 17.75

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

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

Find the length of the missing side.

9

Possible Answers:

\displaystyle 21.57

\displaystyle 13.69

\displaystyle 17.98

\displaystyle 16.58

Correct answer:

\displaystyle 16.58

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

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

Find the length of the missing side.

10

Possible Answers:

\displaystyle 14.52

\displaystyle 17.99

\displaystyle 15.59

\displaystyle 16.23

Correct answer:

\displaystyle 15.59

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

Example Question #17 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

11

Possible Answers:

\displaystyle 18.92

\displaystyle 14.62

\displaystyle 12.68

\displaystyle 16.97

Correct answer:

\displaystyle 16.97

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

Example Question #18 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

12

Possible Answers:

\displaystyle 16

\displaystyle 15

\displaystyle 17

\displaystyle 14

Correct answer:

\displaystyle 15

Explanation:

13

Recall the Pythagorean Theorem for a right triangle:

\displaystyle a^2+b^2=c^2

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

\displaystyle b^2=c^2-a^2

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

Now, plug in values of \displaystyle c and \displaystyle a into a calculator to find the length of side \displaystyle b. Round to \displaystyle 2 decimal places.

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

Example Question #19 : How To Find The Length Of The Side Of A Right Triangle

Tri 3

Given the right triangle above, find the value of \displaystyle x.

Possible Answers:

\displaystyle 1

\displaystyle 4

\displaystyle 9

\displaystyle 3

\displaystyle 2

Correct answer:

\displaystyle 3

Explanation:

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

\displaystyle 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 

\displaystyle 4^2+b^2=5^2 

which can be simplified to 

\displaystyle 16+b^2=25.  

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

\displaystyle 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.

Example Question #20 : 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:

\displaystyle 38

\displaystyle 40

\displaystyle 28

\displaystyle 52

\displaystyle 31

Correct answer:

\displaystyle 40

Explanation:

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

\displaystyle 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 

\displaystyle 9^2+b^2=41^2 

which can be simplified to 

\displaystyle 81+b^2=1681.  

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

\displaystyle 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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