Pythagorean Theorem

a²  +  b²  =  c²

Triangle


Basics
Pythagorean Theorem:  a² + b² = c²
a = altitude = height
b = base
c = hypotenuse

The Pythagorean Theorem applies to a right triangle (a triangle in which one of the angles measures 90°).

Questions involving the Pythagorean Theorem require the calculation of squares and square roots.

square is the squaring command.

2nd square root is the square root command.
2nd activates square root above square .


Formulas (provided by Formula Sheet)

a² + b² = c²


Formulas (NOT provided by Formula Sheet)

c² = a² + b²
c = √

b² = c² – a²
b = √

a² = c² – b²
a = √


Question
In a right triangle, a = 5 and b = 12.  What is c?

Answer
c = 13

Answer Process
c² = a² + b²
c² = 5² + 12²
c² = 25 + 144
c² = 169

c = √
c = √169
c = 13

Calculator Click What You See Comment
clear blinker clears screen
square + 12 square 5²+12² c² = a² + b²
enter 169
2nd square root 169 169 c = √
enter  13 Answer
Pythagorean Theorem


Question
In a right triangle, a = 6 and c = 10.  What is b?

Answer
b = 8

Answer Process
b² = c² – a²
b² = 10² – 6²
b² = 100 – 36
b² = 64

b = √
b = √64
b = 8

Calculator Click What You See Comment
clear blinker clears screen
10 square – 6 square 10²-6² b² = c² – a²
enter 64
2nd square root 64 64 b = √
enter  8 Answer
Pythagorean Theorem


Question
In a right triangle, b = 3 and c = 5.  What is a?

Answer
a = 4

Answer Process
a² = c² – b²
a² = 5² – 3²
a² = 25 – 9
a² = 16

a = √
a = √16
a = 4

Calculator Click What You See Comment
clear blinker clears screen
square – 3 square 5²-3² a² = c² – b²
enter 16
2nd square root 16 16 a = √
enter  4 Answer
Pythagorean Theorem


Question
A right triangular billboard has a height of 6 feet and base of 8 feet.
How long is its hypotenuse?

Answer
10 feet

Answer Process
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100

c = √
c = √100
c = 10

Calculator Click What You See Comment
clear blinker clears screen
square + 8 square 6²+8² c² = a² + b²
enter 100
2nd square root 100 100 c = √
enter  10 Answer
Pythagorean Theorem


Question
A right triangular billboard has a height of 5 feet and hypotenuse of 13 feet.
How long is its base?

Answer
12 feet

Answer Process
b² = c² – a²
b² = 13² – 5²
b² = 169 – 25
b² = 144

b = √
b = √144
b = 12

Calculator Click What You See Comment
clear blinker clears screen
13 square – 5 square 13²-5² b² = c² – a²
enter 144
2nd square root 144 144 b = √
enter  12 Answer
Pythagorean Theorem


Question
A right triangular billboard has a base of 12 feet and hypotenuse of 20 feet.
How high is it?

Answer
16 feet

Answer Process
a² = c² – b²
a² = 20² – 12²
a² = 400 – 144
a² = 256

a = √
a = √256
a = 16

Calculator Click What You See Comment
clear blinker clears screen
20 square – 12 square 20²-12² a² = c² – b²
enter 256
2nd square root 256 256 a = √
enter  16 Answer
Pythagorean Theorem


Question

trianglesnail345
A snail can crawl 4 feet along a wall and then turn 90° to the left and crawl 3 feet along another wall.  If the snail took a straight shortcut from the start to the end of these two walls, how far would the snail crawl?

Answer
5 feet

Answer Process
c² = a² + b²
c² = 3² + 4²
c² = 9 + 16
c² = 25

c = √
c = √25
c = 5

Calculator Click What You See Comment
clear blinker clears screen
square + 4 square 3²+4² c² = a² + b²
enter 25
2nd square root 25 25 c = √
enter  5 Answer
Pythagorean Theorem


Question

trianglesnail345
A snail can crawl 4 feet along a wall and then turn 90° to the left and crawl 3 feet along another wall.  If the snail took a straight shortcut from the start to the end of these two walls, how much shorter was the shortcut than sticking to the walls?

Answer
2 feet

Answer Process
c² = a² + b²
c² = 3² + 4²
c² = 9 + 16
c² = 25

c = √
c = √25
c = 5

Subtract shortcut distance from wall distance.
a + b – c = 3 + 4 – 5 = 2

Calculator Click What You See Comment
clear blinker clears screen
square + 4 square 3²+4² c² = a² + b²
enter 25
2nd square root 25 25 c = √
enter  5 c
3 + 4 – 5 3+4-5 Subtract shortcut from walls.
a + b – c
enter 2 Answer
Pythagorean Theorem

 

Practice – Questions
1.  In a right triangle, a = 10 and b = 24.  What is c?

2.  In a right triangle, a = 50 and c = 130.  What is b?

3.  In a right triangle, b = 30 and c = 50.  What is a?

4.
triangleladder334355
A ladder is leaning against a wall.  Its base is 4.4 meters from the wall.  Its top is 3.3 meters up the wall.  How long is the ladder?

5.
triangleladder668811
A ladder is leaning against a wall.  The ladder is 11 feet long.  Its top is 6.6 feet up the wall.
How long is its base?

6.
triangleladder152025
A ladder is leaning against a wall.  The ladder is 25 feet long.  Its base is 20 feet from the wall.  How high is the ladder up the wall?

7.
2432triangle
A snake can slither 32 feet along a wall and then turn 90° to the left and slither 24 feet along another wall.  If the snake took a straight shortcut from the start to the end of these two walls, how far would the snail slither?

8.  With reference to Question 7, how much shorter was the shortcut than sticking to the walls?

9.
trianglefield6810
A sports fan can run 800 feet along the sideline of a playing field and then turn 90° to the left and run 600 feet along another sideline of a playing field.  At halftime, the sports fan can run a shortcut straight across the playing field from the start to the end of the two sidelines.  What is the distance of this shortcut?

10.  With reference to Question 9, how much longer was sticking to the sidelines than taking the shortcut?


Practice – Answers
1.  c = 26

2.  b = 120

3.  a = 40

4.  5.5 meters

5.  8.8 feet

6.  15 feet

7.  40 feet

8.  16 feet

9.  1000 feet

10.  400 feet

About Scott Solomon

HowtoPasstheGED.com gears up adult learners for the recently redesigned, newly computerized GED. ScottSolomon.com delves into my literary fiction.
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