Applications: Pythagorean Theorem Notes
Key Concept: Identifying Parts of Triangle:
 Legs: 2 sides forming right angle (a, b)
 Hypotenuse: side opposite the right angle; longest side of triangle (c)
Example: Identifying Parts of Triangle
Identify the legs and hypotenuse of the following right triangles:
17
Legs: 8, 15
(make up right ∟)
8
Hypotenuse: 17 (largest # & opposite right ∟)
15
Provided below are lengths of a right triangle. Identify the legs and
hypotenuse.
 6,10, 8 Hypotenuse: 10 (largest), Legs: 6 and 8
 9, 12, 15 Hypotenuse: 15 (largest), Legs: 9 and 12
Practice: Identifying Parts of Triangle
Identify the legs and hypotenuse of the following right triangles:
5
40
12
3
30
5
4
50
13
Provided below are lengths of a right triangle. Identify the legs and
hypotenuse.
a. 12,13, 5 Hypotenuse:____ Legs: __ and ____
b. 9, 12, 15 Hypotenuse:____ Legs:
__ and ____
c. 25, 7, 24 Hypotenuse:____ Legs:
__ and ____
App: Pythagorean Theorem
1
Rev B
Applications: Pythagorean Theorem Notes
Key Concept: Pythagorean Theorem
 Pythagorean theorem: a2 + b2 = c2 (for right angles)
 Pythagorean Theorem is used to find the length of a side of a right
triangle when the lengths of the other 2 sides are known.
if a2 + b2 = c2 then
= √c2 = c
or
if a2 = c2 - b2 then a = √a2 =
if 32 + 42 = 52 then
or
2
if 3 = 52 - 42 then 3 = √32 =
= √52 = 5
Examples: Solve for Missing Side
Using the Pythagorean Theorem, solve for the missing side:
6
x
8
x
Step 1: Identify legs & hypotenuse
Hypotenuse: c = x, Legs: a=6, b=8
Step 2: Plug in values in a2 + b2 = c2 and solve
62 + 82 = x2
36 + 64 = x2
100 = x2
10 = x
17
15
App: Pythagorean Theorem
Step 1: Identify legs & hypotenuse
Hypotenuse: c = 17, Legs: a=x, b=15
Step 2: Plug in values in a2 = c2 - b2 and solve
x2 = 172 - 52
x2 = 289 -225
x2 = 64
x =8
2
Rev B
Applications: Pythagorean Theorem Notes
Practice: Solve for Missing Side
Using the Pythagorean Theorem, solve for the missing side:
1. Solve for a
15
a
12
2. Solve for c
10
3. Solve for b
24
2
6
c
b
4. Solve for a
10
a
8
5. Solve for c
5
6. Solve for b
12
4
6
c
b
Key Concept: Determining if lengths are sides of right triangle
 When given 3 sides, identify your hypotenuse and legs with the
hypotenuse being the largest number.
 Plug in values into the Pythagorean Theorem: a2 + b2 = c2
 If the equation is true, then you have a right triangle
 If a2 + b2 > c2 then you have an acute triangle
 If a2 + b2 < c2 then you have an obtuse triangle
Examples: Determining if lengths are sides of right triangle
Determine whether the given lengths are sides of a right triangle.
a. 3, 9, 7
b. 6,10, 8
hypotenuse: 9; legs: 3, 7
hypotenuse: 10; legs 6, 8
2
2
2
3 +7 =9
62 + 82 = 102
9 + 49 = 81
36 + 64 = 100
58 ≠ 81
100 = 100
No, obtuse triangle
Yes
App: Pythagorean Theorem
3
Rev B
Applications: Pythagorean Theorem Notes
Practice: Determining if lengths are sides of right triangle
Determine whether the given lengths are sides of a right triangle.
a. 20, 21, 29
b. 16,30,34
c. 7, 24, 25
d. 24, 60, 66
e. 23,18,14
f. 9, 12, 15
Key Concept: Pythagorean Triples
There are many common sets of 3 whole numbers that satisfy the
Pythagorean Theorem. Memorize the following Pythagorean Triples. They
come in handy and help save you time.
 3, 4, 5
 5, 12, 13
 7, 24, 25
 8, 15, 17
 9, 40, 41
NOTE: The largest number must be the hypotenuse in order for these to
work.
Key Concept: Special Right Triangles
App: Pythagorean Theorem
4
Rev B