Interactive tutorial for solving for all missing sides of right triangle with Pythagorean Theorem.

1. Using the Pythagorean Theorem
Sarah Katko ICL 7062

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The Pythagorean Theorem is the formula
used to find the missing side of a right triangle.
The purpose of this tutorial is to thoroughly
explain/illustrate how to solve problems through
the application of this theorem. There will be
opportunities for you to practice this skill
throughout this module. You may use the
navigation bar at on the left of this home screen
to jump to specific sections of this tutorial. To
access the bar throughout the tutorial, simply
press the home button in the bottom of any
screen to return to this page. When you are
finished with this tutorial, you will demonstrate
the ability to solve for the missing side of a right
triangle with at least 80% mastery.
The Pythagorean Theorem is the formula
used to find the missing side of a right triangle.
The purpose of this tutorial is to thoroughly
explain/illustrate how to solve problems through
the application of this theorem. There will be
opportunities for you to practice this skill
throughout this module. You may use the
navigation bar at on the left of this home screen
to jump to specific sections of this tutorial. To
access the bar throughout the tutorial, simply
press the home button in the bottom of any
screen to return to this page. When you are
finished with this tutorial, you will demonstrate
the ability to solve for the missing side of a right
triangle with at least 80% mastery.
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The formula for the Pythagorean Theorem is:
We can use this formula to find the length of a missing side of a right triangle.
The formula for the Pythagorean Theorem is:
We can use this formula to find the length of a missing side of a right triangle.
A right triangle is
made up of three
sides: two legs and
a hypotenuse.
“A” represents one
leg of the right
triangle, and ”B”
represents the other
leg. The third side
is the hypotenuse,
and it is the longest
side. The
hypotenuse is
represented by the
letter “C” in the
formula.
A right triangle is
made up of three
sides: two legs and
a hypotenuse.
“A” represents one
leg of the right
triangle, and ”B”
represents the other
leg. The third side
is the hypotenuse,
and it is the longest
side. The
hypotenuse is
represented by the
letter “C” in the
formula.
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It is imperative to correctly identify the sides of the triangle, so that the numbers are in the correct
place in the formula. While the legs are interchangeable (it does not matter if you switch “A” and “B”
around), the hypotenuse must always be “C”.
***The hypotenuse is ALWAYS the longest side in the right
triangle.****
A helpful hint for determining the hypotenuse is to locate the right angle, which is marked and
indicated by a small box. Use the right angle symbol there to create an arrow. The arrow will always
point to the hypotenuse!
It is imperative to correctly identify the sides of the triangle, so that the numbers are in the correct
place in the formula. While the legs are interchangeable (it does not matter if you switch “A” and “B”
around), the hypotenuse must always be “C”.
***The hypotenuse is ALWAYS the longest side in the right
triangle.****
A helpful hint for determining the hypotenuse is to locate the right angle, which is marked and
indicated by a small box. Use the right angle symbol there to create an arrow. The arrow will always
point to the hypotenuse!

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Now that we have the basic information, lets see how this works. In the right triangle below, all sides are
measured, so we will use the Pythagorean Theorem to check for accuracy.
We will use our formula to plug in numbers correctly. First, I can identify my legs (A and B) as 3 and 4. The
hypotenuse (longest side) is labeled 5, and I can draw an arrow in my right angle symbol to make sure it is
indeed the hypotenuse.
Now, I will plug my legs in for A and B and my hypotenuse in for C.
a2
+b2
= c2
32
+ 42
= 52
Next, I will square the numbers
a2
(3 x 3) = 9
b2
(4 x 4) = 16
c2
(5 x 5) = 25
Last, I will plug the numbers into the formula and make sure
both sides are equal.
a2
+b2
= c2
9 + 16 = 25 ✔
Since both sides are equal, we know this is correct!
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a2
+b2
= c2
therefore 32
+42
= c2
Now, we will square the numbers and plug them back into the
formula.
32
= 9 and 42
= 16
9 + 16 = c2
9 + 16 = 25 therefore 25 = c2
If c2
is 25, and we want to solve for C, we must undo the square by
doing the opposite. We must find the square root of 25.
√25 = 5, therefore 5 is C
Just to be sure, let’s check:
a2
+b2
= c2
32
+42
= 52
9 + 16 = 25 ✔
Let’s apply what we have just learned to solve for C, the hypotenuse. In the picture below, we can see that the point
of the arrow is indeed pointing to the longest side, which is missing its measurement. Therefore, we know that we
are solving for C. Our legs are labeled with numbers to be placed in the formula for the Pythagorean Theorem.
Let’s apply what we have just learned to solve for C, the hypotenuse. In the picture below, we can see that the point
of the arrow is indeed pointing to the longest side, which is missing its measurement. Therefore, we know that we
are solving for C. Our legs are labeled with numbers to be placed in the formula for the Pythagorean Theorem.
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A. 10 feet
B. 14 feet
C. 25 Feet
D. 100 feet
Let’s try a contextual problem with a little guidance. Your sides have been identified for you, so plug them
into the formula first. Remember: a2
+b2
= c2
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Side “A” is 8Side “A” is 8
Side “B” is 6Side “B” is 6
Square sides A and B, then add them together. Find the square root of the total, and that is the length of side C!
Once you get your answer, proceed to the next slide for an explanation.

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A. 10 feet
B. 14 feet
C. 25 Feet
D. 100 feet
If you got A, 10 feet for your answer, you are correct!
Explanation: a2
+b2
= c2
The branches are leaning against the wall, which is side C.
The ground where the sleeping bag is 6 feet long, and the
wall it is against is 8 feet tall. These numbers represent
the legs, A and B.
Steps:
Plug in the sides : 62
+ 82
=c2
Square and add together: 36 + 64 = c2
Add A and B together: 36 + 64 = 100
Since 100 represents c2
we must do the opposite or
inverse
of squaring, which is finding the square root.
√100 = 10
Check: 62
+ 82
= 102
36 + 64 = 100 ✔
Both sides are equal, so it balances the equation!
Hint: looking at the
answer choices, we
can automatically
rules out choice D.
This is way too large of
a number if one side is
6 and the other is 8.
Test writers expect
students to choose
this answer because it
is the in the process,
but not the final
answer! Be careful!
Hint: looking at the
answer choices, we
can automatically
rules out choice D.
This is way too large of
a number if one side is
6 and the other is 8.
Test writers expect
students to choose
this answer because it
is the in the process,
but not the final
answer! Be careful!

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A) 16.7 units
B) 4.5 units
C) 8.9 units
D) 14.4 units
A) 16.7 units
B) 4.5 units
C) 8.9 units
D) 14.4 units
It’s time to do one on your own! If you need help with the steps, press the button to return to the previous
slide. HINT: since you are solving for the longest side, there are two answers that can automatically be
ruled out. Once you have solved for side c, click on the answer you have chosen for feedback.
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A) 10.23 feet
B) 16.09 feet
C) 23.59 feet
D) 26.63 feet
A) 10.23 feet
B) 16.09 feet
C) 23.59 feet
D) 26.63 feet
Time to try one more before moving on to solving for a missing leg! If you are still feeling confused, or
would just like additional information, please click on the link to watch the video for further explanation:
khan academy pythagorean theorem . The last four minutes of the video will lead you into the next part
of our lesson.
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Now that we have used the Pythagorean Theorem to solve for a missing hypotenuse, will move on to
solving for a missing leg. To do this we will begin the same way, by plugging what we have into the formula:
a2
+b2
= c2
262
+ b2
= 522
Now, square the numbers and plug the answers back into the formula:
262
= 676 and 522
= 2704 therefore 676 + b2
= 2704
Now we will apply what we know about solving equations (performing inverse operations ) to get “b” by itself.
676 + b2
= 2704
-676 -676
b2
= 2028
The “b” is still squared, so we must find the square root of each side to get it alone.
√ b = √2028 therefore b= 45 mm
Now that we have used the Pythagorean Theorem to solve for a missing hypotenuse, will move on to
solving for a missing leg. To do this we will begin the same way, by plugging what we have into the formula:
a2
+b2
= c2
262
+ b2
= 522
Now, square the numbers and plug the answers back into the formula:
262
= 676 and 522
= 2704 therefore 676 + b2
= 2704
Now we will apply what we know about solving equations (performing inverse operations ) to get “b” by itself.
676 + b2
= 2704
-676 -676
b2
= 2028
The “b” is still squared, so we must find the square root of each side to get it alone.
√ b = √2028 therefore b= 45 mm
Side C
Side A
Side B

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.
A) 6
B) 8
C) 9
D) 10
A) 6
B) 8
C) 9
D) 10
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Solve the problem and click on the answer you have selected for feed back. Use the following steps
to try it on your own:
Plug numbers into formula, paying close attention to identifying the hypotenuse (C).
Square the numbers and plug back into formula.
Solve the equation by performing inverse operations.
Do not forget to find the square root at the end!

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A) 9 units
B) 20 units
C) 40 units
D) 80 units
A) 9 units
B) 20 units
C) 40 units
D) 80 units
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Solve for the missing leg and click your answer for feedback. Feel free to visit the previous
slides for help.
Hint!

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A) 3.2 feet
B) 10.5 feet
C) 33.2 feet
D) 78.1 feet
A) 3.2 feet
B) 10.5 feet
C) 33.2 feet
D) 78.1 feet
home
Solve for the missing leg and click your answer for feedback.

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Congratulations, you have successfully completed the module!
For additional practice with the Pythagorean Theorem, click here:
practice problems
If you are ready to take an assessment on the Pythagorean Theorem
click here : Discovery Log In
Enter your last name, leave a space, and enter your first name. Enter this
code: PZPUQ203087
You will get to choose a game to play for correct answers and feedback will
be given.
Good luck!

16. Awesome work! You are correct!
Click below to return to the
last slide viewed and then
move on to the next slide.

17. Press the button to return to the
slide and try again.
Press the button to return to the
slide and try again.
Make sure you have plugged everything
in correctly by using the diagram.
After squaring the numbers and adding them
together, find the square root of the total.

18. Remember the steps!
Plug numbers into formula, paying close attention to identifying the hypotenuse (C). DO YOU HAVE
NUMBERS ON BOTH SIDES OF THE EQUATION?
Square the numbers and plug back into formula.
Solve the equation by performing inverse operations. THIS MEANS SUBTRACT FROM BOTH SIDES!
Do not forget to find the square root at the end!
Press the button to return to the
slide and try again.
Press the button to return to the
slide and try again.