1. Pythagorean Relationship 2 (Finding the length of the Hypotenuse)
Measurement
Pythagorean Relationship 2
(Finding the length
of the Hypotenuse)

2. To review…
In a right angle triangle, the side of the triangle opposite the right angle is called the hypotenuse.
hypotenuse
legs

3. Pythagorean Relationship
Area = c2 b c
Area = b2 c b a
a2 + b2 = c2 a
Area = a2

4. Applying the Pythagorean Relationship
We know that:
a b2 = c2 a c b

5. Applying the Pythagorean Relationship
Using this…
If we know the lengths of ANY two sides of a right angle triangle, we can use the Pythagorean Relationship to find the length of the unknown side. a c b

6. Applying the Pythagorean Relationship
Situation One:
We know the lengths of the two legs (a and b) of a right triangle.
How can we find the length of the hypotenuse (c)? a c b

7. Applying the Pythagorean Relationship
Since we know that:
a2 + b2 = c2
Then:
c2 = a2 + b2 a c b

8. Applying the Pythagorean Relationship
Since:
c2 = a2 + b2
Then:
c = (a2 + b2) a c b

9. Applying the Pythagorean Relationship
Example: a = 7m; b = 5m
c = (a2 + b2)
c = ( )
c = ( )
c =
c = m
a = 7m
c = ?
b = 5m

10. Problem
a = 3cm
Find the length of the hypotenuse, “c”.
b = 6cm
c = ?