Pythagorean TheoremSolving Right Triangles

Solving Right Triangles Directions

As you view this presentation, take notes and work out the practice problems.

When you get to the practice problem screens, complete the step in your notebook before continuing to the next slide.

The Right Triangle

• A right triangle has one 90o

angle, A 90o angle is also called a right angle. You know which angle is the right angle because it will have a box at the angle.

• The side across from the right angle is called the hypotenuse and is usually labeled with the letter c,

• The other two sides are called legs and are usually labeled with the letters a and b.

ca

b

Pythagorean Theorem

• The mathematician Pythagoras proved the relationship between the sides of a right triangle and the hypotenuse. This relationship is known as the Pythagorean Theorem

c

b

a

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 12

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 12122 +52 = c2

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: 122 + 52 = c2

c = ?

b = 5

a = 12

Step 2: Do the math.

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: 122 + 52 = c2

c = 13

b = 5

a = 12

Step 2: Do the math.

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 6

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 662 + 52 = c2

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: 62 + 52 = c2

c = ?

b = 5

a = 6

Step 2: Do the math.

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: 62 + 52 = c2

b = 5

a = 6

Step 2: Do the math.Note: c2 is not always a perfect square. Always read directions carefully to know what form your answer should take.

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = ?

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = ?

a2 + 82 = 102

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = ?

a2 + 82 = 102

Step 2: Do the math.

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = 6

a2 + 82 = 102

Step 2: Do the math.

a2 + 64 = 100

a2 = 36

a = 6

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: Substitute the values of b and c into a2 + b2 = c2.

c = 9b = ?

a = 5

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: Substitute the values of b and c into a2 + b2 = c2.

c = 9 b = ?

a = 5

52 + b2 = 92

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: 52 + b2 = 92.

c = 9 b = ?

a = 5

Step 2: Do the math.

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: 52 + b2 = 92.

c = 9

a = 5

Step 2: Do the math.

Note: You should always simplify the square root if possible.