Geometry
WARM UP Right Triangles Day 2
Find the unknown side length. No decimals!
1.
x
3
9
3.
Name_______________________________
2.
18
10
x
14
4
x
Classify the triangle formed by the side lengths as acute, right, or obtuse.
4. 6, 7, and 9
5. 10, 12, and 16
6. 8, 16, and 8 6
7. 20, 21, and 29
Today you will:
 Learn about Pythagorean Triples and how they can help you to quickly find missing side lengths in
right triangles. You will also learn how to solve word problems involving right triangles.
 At the end of class, you will solve right triangle word problems using the Pythagorean Theorem.
More Pythagorean Theorem
Pythagorean triple –
Common Pythagorean Triples and Some of Their Multiples
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
6, 8, 10
10, 24, 26
16, 30, 34
14, 48, 50
9, 12, 15
15, 36, 39
24, 45, 51
21, 72, 75
30, 40, 50
50, 120, 130
80, 150, 170
70, 240, 250
3x, 4x, 5x
5x, 12x, 13x
8x, 15x, 17x
7x, 24x, 25x
Example 1
Find the unknown side length of the right triangle using the Pythagorean Theorem. Then show how to
reduce it down to its common Pythagorean triple.
12
9
x
Example 2
Find the unknown side length of the right triangle using the Pythagorean Theorem. Then show how to
reduce it down to its common Pythagorean triple.
x
14
48
The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers and
together form a Pythagorean triple. Determine the length of the third side and tell whether it is a leg or the
hypotenuse.
3. 24 and 51
4. 20 and 25
5. 28 and 96
6. 20 and 48
More Word Problems!!!
7. A wall is supported by a brace 10 feet long, as shown in the diagram. If one end of the brace is placed 6
feet from the base of the wall, how many feet up the wall does the brace reach?
8. How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder
will reach a point on the house 36 feet from the ground?
9. The end of a dog’s leash is attached to the top of a 5-foot-tall fence post, as shown in the diagram. The
dog is 7 feet away from the base of then fence post. How long is the leash?
10. A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the
base of the flagpole. How tall is the flagpole?
11. If the length of a rectangular television screen is 20 inches and its height is 15 inches, what is the
length of its diagonal, in inches?
12. A builder is building a rectangular deck with dimensions of 16 feet by 30 feet. To ensure that the sides
form 90° angles, what should each diagonal measure?