Study Guide and Intervention (continued) - MathnMind

11-4
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Study Guide and Intervention
The Pythagorean Theorem
The Pythagorean Theorem The side opposite the right angle in a right triangle is
called the hypotenuse. This side is always the longest side of a right triangle. The other
two sides are called the legs of the triangle. To find the length of any side of a right
triangle, given the lengths of the other two sides, you can use the Pythagorean Theorem.
Pythagorean Theorem
Find the length of the
hypotenuse of a right triangle if a 5
and b 12.
c2 a2 b2 Pythagorean Theorem
c2 52 122 a 5 and b 12
c2 169 Simplify.
c 169 Take the square root of each side.
c 13
The length of the hypotenuse is 13.
If a and b are the measures of the legs of a right triangle
and c is the measure of the hypotenuse, then c 2 a 2 b 2 .
Example 1 Example 2
Exercises
Find the length of a leg
of a right triangle if a 8 and c 10.
c2 a2 b2 Pythagorean Theorem
102 82 b2 a 8 and c 10
100 64 b2 Simplify.
36 b2 Subtract 64 from each side.
b 36 Take the square root of each side.
b 6
The length of the leg is 6.
Find the length of each missing side. If necessary, round to the nearest
hundredth.
1. 2. 3.
30
40
c
If c is the measure of the hypotenuse of a right triangle, find each missing
measure. If necessary, round to the nearest hundredth.
110
100
4. a 10, b 12, c ? 5. a 9, b 12, c ? 6. a 12, b ?, c 16
7. a ?, b 6, c 8 8. a ?, b 8, c 18 9. a 5, b 10, c ?
© Glencoe/McGraw-Hill 661 Glencoe Algebra 1
a
c
25
a
B
C
25
c
b
A
Lesson 11-4