Page 574 - Algebra 1

Example
3
Application: Length of a Ladder
The ladder in the diagram satisfies the “1 in 4 rule,” a rule
of thumb for the safe use of ladders. This rule states that
when the bottom of a ladder is positioned x feet from the
base of a building, the top of the ladder should reach a c point 4x feet off the ground. Find the length of the ladder
in the diagram. Round your answer to the nearest tenth of a foot.
SOLUTION
20 ft
Math Reasoning
Analyze The bottom of a ladder that satisfies the
1 in 4 rule is 3 feet from the base of a building. Find the length of the ladder.
The ladder is the hypotenuse of a right triangle. The lengths of the legs of the triangle are 5 feet and 20 feet. Use the Pythagorean Theorem to find the length c of the ladder.
a2 + b2 = c2 52 + 202 =c2 425 =c2
√ 42 5 =c 5 √ 17 =c 20.6 ≈c
Substitute 5 for a and 20 for b.
Simplify the left side.
Take the positive square root of each side. Simplify the square root.
Estimate; round to the nearest tenth.
The length of the ladder is 20.6 feet.
Use the Pythagorean Theorem to find the missing side lengths.
5 ft
Lesson Practice
(Ex. 1)
a. Find side length c.
16
12
c
b. Find side length m to the nearest tenth. 11
2
c. Find side length r.
m
√85
6
r
d. Find side length s in simplest radical form.
9
3
s
Lesson 85 559