(8) Lesson 5.6 - Use the Pythagorean Theorem

1. Course 3, Lesson 5-6
Write an equation you could use to find the length of the missing
side of each right triangle. Then find the missing length.
1. 2. 3.
4. Is a triangle with side lengths of 18, 25, and 33 a right triangle?
5. A man drives 33 miles east and 12 miles south. What is the shortest
distance between the man and his starting point?

2. Course 3, Lesson 5-6
ANSWERS
1. 32 + 42 = x2; 5 cm
2. 152 + x2 = 252; 20 ft
3. x2 + 122 = 132; 5 in.
4. no
5. 35

3. HOW can algebraic concepts be
applied to geometry?
Geometry
Course 3, Lesson 5-6

4. Course 3, Lesson 5-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 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.
• 8.EE.2
Use square root 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.

5. Course 3, Lesson 5-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

6. To
• apply the Pythagorean Theorem to find
unknown side lengths in right triangles
in real-world situations,
• use the Pythagorean Theorem to find
missing measures in three-dimensional
figures
Course 3, Lesson 5-6
Geometry

7. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
1. Write an equation that can be used to find the
length of the ladder. Then solve. Round to the
nearest tenth.
Pythagorean Theorema2 + b2 = c2
Replace a with 8.75 and b with 18.
76.5625 + 324 = c2
Notice that the distance from the building, the
building itself, and the ladder form a right
triangle. Use the Pythagorean Theorem.
8.752 + 182 = c2
Evaluate 8.752 and 182.
400.5625 = c2 Add 76.5625 and 324.
Definition of square root
Use a calculator.±20.0 ≈ c
Since length cannot be negative, the ladder is about 20 feet long.
±√400.5625 = c

8. Answer
Need Another Example?
Write an equation that can be
used to find the length of the
boat ramp. Then solve. Round
to the nearest tenth.
4.22 + 252 = c2; 25.4 ft

9. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
2. Write an equation that can be used to find the
height of the plane. Then solve. Round to the
nearest tenth.
Pythagorean Theorema2 + b2 = c2
Replace a with 10 and c with 12.
100 + b2 = 144
The distance between the planes is the
hypotenuse of a right triangle. Use the
Pythagorean Theorem.
102 + b2 = 122
Evaluate 102 and 122.
b2 = 44 Subtraction Property of Equality
Since length cannot be negative, the height of the plane is about 6.6 miles.
Definition of square root
Use a calculator.b ≈ ±6.6
b = ±√44

10. Answer
Need Another Example?
Write an equation that can be
used to find the length of the
backboard. Then solve. Round to
the nearest tenth.
422 + x2 = 83.42; 72.1 in.

11. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. A 12-foot flagpole is placed in the center of a
square area. To stabilize the pole, a wire will
stretch from the top of the pole to each corner of
the square. The flagpole is 7 feet from each corner
of the square. What is the length of each wire?
Round to the nearest tenth.
Pythagorean TheoremAB2 + AC2 = BC2
Replace AB with 7 and AC with 12.
49 + 144 = BC2
Draw right triangle ABC. You want to find the length of
each wire or BC. This is the hypotenuse of a right
triangle, so use the Pythagorean Theorem.
72 + 122 = BC2
Evaluate 72 and 122.
193 = BC2 Simplify
Since length cannot be negative, the length of the wire is about 13.9 feet.
Definition of square root
Use a calculator.±13.9 ≈ BC
±√193 = BC

12. Answer
Need Another Example?
The slant height of a pyramid is the
height of each lateral face. What is
the slant height of the pyramid
shown? Round to the nearest tenth.
11.7 cm

13. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-6
Geometry

14. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-6
Geometry
Sample answer:
• You write and solve equations using the Pythagorean
Theorem to find missing lengths in real-world
situations involving right triangles.

15. How do you think using
the Pythagorean Theorem will
connect with the next lesson
about finding the distance
between two points on
the coordinate plane?
Ratios and Proportional RelationshipsFunctionsGeometry
Course 3, Lesson 5-6