Real Numbers And The Pythagorean Theorem Worksheet - Chapter 7 Page 18
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46Finding the Length of a Leg
2 2
EXAMPLE
Find the missing length of the triangle.
2
+
2
=
2
a
b
c
Write the Pythagorean Theorem.
2
+
2
=
2
a
2.1
2.9
Substitute 2.1 for b and 2.9 for c.
a
2.1 cm
2
+ 4.41 = 8.41
a
Evaluate powers.
2
= 4
a
Subtract 4.41 from each side.
2.9 cm
a = 2
Take positive square root of each side.
The missing length is 2 centimeters.
3 3
Real-Life Application
EXAMPLE
You are playing capture the fl ag. You are 50 yards north and 20 yards
east of your team’s base. The other team’s base is 80 yards north and
60 yards east of your base. How far are you from the other team’s base?
Step 1: Draw the situation in a coordinate plane. Let the origin
N
90
represent your team’s base. From the descriptions, you are
Other Base
(60, 80)
80
at (20, 50) and the other team’s base is at (60, 80).
70
30 yd
60
Step 2: Draw a right triangle with a hypotenuse that represents the
You
50
distance between you and the other team’s base. The lengths
40 yd
(20, 50)
40
of the legs are 30 yards and 40 yards.
30
20
Step 3: Use the Pythagorean Theorem to fi nd the length of the
10
hypotenuse.
Your Base
W
10 20 30 40 50 60 70 80
E
2
2
2
+
=
a
b
c
Write the Pythagorean Theorem.
S
2
+
2
=
2
30
40
c
Substitute 30 for a and 40 for b.
900 + 1600 = c
2
Evaluate powers.
2500 = c
2
Add.
50 = c
Take positive square root of each side.
So, you are 50 yards from the other team’s base.
Find the missing length of the triangle.
Exercises 5–8
4.
3.
9.6 m
a
34 yd
16 yd
10.4 m
b
5. In Example 3, what is the distance between the bases?
Section 7.3
The Pythagorean Theorem
303
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