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Finding the Length of the Hypotenuse in Right Triangles, Lecture notes of Analytical Geometry and Calculus

Instructions and examples on how to find the length of the hypotenuse in right triangles using the Pythagorean Theorem. It covers identifying the legs and hypotenuse, understanding the theorem, and solving practice problems.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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7.2 Find the Length of the
Hypotenuse
Common Core Standards
8. EE.2 Use square root and cube root symbols to represent solutions to
equations of the form x2 = p and x3 = 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.
8. G.6 Explain a proof of the Pythagorean Theorem and its converse.
8. 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
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7.2 Find the Length of the

Hypotenuse

Common Core Standards

  1. 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.

  1. G.6 Explain a proof of the Pythagorean Theorem and its converse.
  2. 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

  1. 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.