The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples A right triangle has legs of length 16 and 30.
Download ReportTranscript The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples A right triangle has legs of length 16 and 30.
The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples
A right triangle has legs of length 16 and 30. Find the length of the hypotenuse. Do the lengths of the sides form a Pythagorean triple?
a
2 +
b
2 =
c
2 16 2 + 30 2 =
c
2 256 + 900 =
c
2 1156 =
c
2 Use the Pythagorean Theorem.
Substitute 16 for
a
and 30 for
b
.
Simplify.
34 =
c
Take the square root.
The length of the hypotenuse is 34. The lengths of the sides, 16, 30, and 34, form a Pythagorean triple because they are whole numbers that satisfy
a
2 +
b
2 =
c
2 . Notice that each length is twice the common Pythagorean triple of 8, 15, and 17.
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The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples
form.
Find the value of
x
. Leave your answer in simplest radical
a
2 +
b
2 =
c
2
x
2 + 10 2 = 12 2
x
2 + 100 = 144
x
2 = 44
x
= 4(11)
x
= 2 11
HELP
Use the Pythagorean Theorem.
Substitute
x
for
a
, 10 for
b
, and 12 for
c
.
Simplify.
Subtract 100 from each side.
Take the square root of each side.
Simplify.
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The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples
A baseball diamond is a square with 90-ft sides. Home plate and second base are at opposite vertices of the square. About how far is home plate from second base?
Use the information to draw a baseball diamond.
a
2 +
b
2 =
c
2 90 2 + 90 2 =
c
2 8100 + 8100 =
c
2 16,200 =
c
2 Use the Pythagorean Theorem.
Substitute 90 for
a
Simplify.
and for
b
.
c
= 16,200 Take the square root.
c
Use a calculator.
The distance to home plate from second base is about 127 ft.
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The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples
Is this triangle a right triangle?
a
2
+
b
2
c
2
4
2
+ 6
2
7
2
Substitute 4 for
a,
6 for
b,
and 7 for
c.
16 + 36 49 Simplify.
52 ≠ 49 Because
a
2
+
b
2
≠
c
2
,
the triangle is not a right triangle.
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The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples
The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse, or right.
a.15, 20, 25 c
2
25
2
a
2
+
b
2
Compare
c
2
with
a
2
+
b
2
.
15
2
+ 20
2
Substitute the greatest length for
c.
625 225 + 400 Simplify.
625 = 625 Because
c
2
=
a
2
+
b
2
, the triangle is a right triangle.
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The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples (Continued)
b. 10, 15, 20
c
2
a
2
+
b
2
20
2
10
2
+ 15
2
Compare
c
2
400 100 + 225 Simplify.
400 325 with
a
2
+
b
2
.
Substitute the greatest length for
c.
Because
c
2
a
2
+
b
2
, the triangle is obtuse.
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