Lesson 3-4
Example 1 Find the Length of a Hypotenuse
KITES Find the length of the kite string.
The kite string forms the hypotenuse of a right triangle. The vertical and horizontal
distances form the legs.
c2  a2  b2
c 2  60 2  80 2
c 2  3,600  6,400
c 2  10,000
Pythagorean Theorem
Replace a with 60 and b with 80.
Evaluate 602 and 802.
Add 3,600 and 6,400.
c 2  10,000
c = 100 or –100
Take the square root of each side.
Simplify.
The equation has two solutions, 100 and –100. However, the length of the kite string must be
positive. So, the kite string is 100 feet long.
Example 2 Find the Length of a Leg
The hypotenuse of a right triangle is 15 inches long and one of its legs is 11 inches. Find the
length of the other leg.
c2  a2  b2
152  a 2  112
225  a 2  121
225  121  a 2  121  121
104  a 2
104  a 2
10.2  a
Pythagorean Theorem
Replace c with 15 and b with 11.
Evaluate 152 and 112.
Subtract 121 from each side.
Simplify.
Take the square root of each side.
Use a calculator.
The length of the other leg is about 10.2 inches.
Example 3 Use the Pythagorean Theorem
MULTIPLE-CHOICE TEST ITEM The base of a 32-foot ladder is 10 feet from the wall.
How high can this ladder reach?
A about 30.4 feet
B about 33.5 feet
C about 85.8 feet
D about 220 feet
Read the Test Item You know the length of the ladder and the distance from the base of the
ladder to the wall. Make a drawing of the situation including the right triangle.
Solve the Test Item Use the Pythagorean Theorem
Pythagorean Theorem
c2  a2  b2
2
2
2
Replace c with 32 and b with 10.
32  a  10
2
Evaluate 322 and 102.
1,024  a  100
1,024  100  a 2  100  100 Subtract 100 from each side.
Simplify.
924  a 2
924  a 2
30.4  a
Take the square root of each side.
Use a calculator.
The ladder can reach a height of 30.4 feet. The answer is A.
Example 4 Identify a Right Triangle
The measures of three sides of a triangle are 30 inches, 16 inches, and 34 inches. Determine
whether the triangle is a right triangle.
c2 = a2 + b2
Pythagorean Theorem
?
342  162 + 302
?
1,156  256 + 900
1,156 = 1,156 
c = 34, a = 16, b = 30.
Evaluate 342, 162, and 302.
Simplify.
The triangle is a right triangle.