Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #90 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse using Pythagorean Theorem.

The triangle has two other sides with lengths 3 and 4 inches.

Possible Answers:

Correct answer:

Explanation:

The formula for Pythagorean Theorem is, 

C is the hypotenuse and A and B are the other two sides. To begin Pythagorean Theorem the order of A and B does not matter.

If A is 3 and B is 4 then,

You must find C and not c squared. Therefore to get rid of the squared you must do the opposite of squaring something, which is the square root of something. 

5 inches

Example Question #21 : 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.

9

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 ,

13

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

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

Simply:

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Justin travels  to the east and  to the north. How far away from his starting point is he now?

Possible Answers:

Correct answer:

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that  

  

 

Example Question #134 : Right Triangles

A right triangle has side lengths of 20 inches and 19 inches. What is the length of its hypotenuse?

Possible Answers:

None of these.

Correct answer:

Explanation:

We can find any one missing side of a right triangle with the Pythagorean theorem. 

Simplify and take the square root of both sides:

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 2

Given the right triangle above, find the length of the hypotenuse.

Possible Answers:

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

.  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

 

and 

.  

Next, we must add these two solutions to get .  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

.

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 1

Given the right triangle above, find the length of the hypotenuse.

Possible Answers:

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

.  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

 

and 

.  

Next, we must add these two solutions to get .  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

.

Example Question #94 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 4

Find the length of the hypotenuse of the right triangle.

Possible Answers:

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

.  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

 

and 

.  

Next, we must add these two solutions to get .  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

.  

This example is another instance of a Pythagorean triple to keep in mind.

Example Question #136 : Right Triangles

Tri 7

Find the length of the hypotenuse of the right triangle.

Possible Answers:

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

.  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

 

and 

.  

Next, we must add these two solutions to get .  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

Example Question #95 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 10

Find the length of the hypotenuse of the right triangle.

Possible Answers:

Correct answer:

Explanation:

To find the length of the hypotenuse, we will use the Pythagorean Theorem

.  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

 

and 

.  

Next, we must add these two solutions to get .  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

.

Example Question #92 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Tri 12

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

Possible Answers:

Correct answer:

Explanation:

Using the Pythagorean Theorem

,

we can find the length of the hypotenuse in terms of variables.  

First, square both given sides and add them together.  Next, take the square root of that sum to find the length of the hypotenuse in terms of s.  

The calculation should look like this: 

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