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7.2 Find the Length of the
Hypotenuse
Common Core Standards
- EE.2 Use square root and cube root symbols to represent solutions to
equations of the form x
2
= p and x
3
= p, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots of
small perfect cubes. Know that √ 2 is irrational.
- G.6 Explain a proof of the Pythagorean Theorem and its converse.
- G.7 Apply the Pythagorean Theorem to determine unknown side lengths
in right triangles in real-world and mathematical problems in two and three
dimensions
WARM-UP
- Only copy the right triangle.
Copy the right triangles and circle the length of the
hypotenuse.
116
o 85
o
57
o
38
o
NOTES
The two short sides of a right triangle are called the legs.
The longest side is called the hypotenuse.
Examples
Identify the hypotenuse and the legs of the right
triangles.
F
E
D
L
K
J
B
A
C
NOTES
The Pythagorean Theorem:
The sum of the squares of the two legs of a right
triangle always equals the square of the hypotenuse.
Examples
Find the length of the hypotenuse.
2 2 2
leg + leg = hyp
NOTES
The hypotenuse must be the longest side.
Examples
Eliminate the answers that are not possible values
for the hypotenuse.
Find the length of the
hypotenuse.
a) 8 b) 15 c) 25 d)
EXAMPLES
Find the length of the hypotenuse.
PRACTICE
A ladder leans against a wall. The top of the ladder is 8
feet from the ground. The bottom of the ladder is 6
feet from the wall. How long is the ladder?
9 ft
12 ft
PRACTICE
Find the length of the hypotenuse of a right triangle
if the two legs are 15 inches and 20 inches.
PRACTICE
Find the length of the hypotenuse. Round your answer
to the nearest tenth.
NOTES
Example
Find the length of the hypotenuse. Round your answer
to the nearest whole number.
There are very few right triangles in which all three
sides have whole number lengths.
