Algebra 1 Common Core Student Edition, Grade 8-9

Pl o n t

What do you know?

What do you need?

You k n o w th e lengths

a and b o f th e tw o

legs. You need to

find the length c

o f th e hypotenuse.

Substitute for a and b in

a2 + b2 = c2, and then

solve for c.

H o w is th is p ro b le m
different from
P ro b le m 1?
In Problem 1, th e length
of the hypotenuse
w as u n k n o w n. In th is
problem, the length of a
leg is u n kn o w n.

You can use the Pythagorean Theorem to find the length of a right triangle's hypotenuse

given the lengths of its legs. Using the Pythagorean Theorem to solve for a side length

involves finding a principal square root, because side lengths are always positive.

Pr o b l em 1 Finding the Length of a Hypot enuse

The tiles at the right are squares with 6-in.

sides. What is the length of the hypotenuse

of the right triangle shown?

Pythagorean Theorem

Substitute 6 for a and b.

Simplify.

a2 + b2 = c2

62 + 62 = c2

72 = c2

V72 = c Find the principal square

root.

8.5 = c Use a c a lc u la to r.

The length of the hypotenuse is about 8.5 in.

vj Got It? 1. What is the length of the

hypotenuse of a right triangle

with legs of lengths 9 cm and

12 cm?

You can also use the Pythagorean Theorem to find the length of a leg of a right triangle.

Finding t he Length of a Leg

What is the side length b in the triangle at the right?

a2 + b2 = c2

5 2 + b 2 = 132

25 + b2= 169

b2 = 144

b— 12

Pythagorean Theorem

S u b s titu te 5 f o r a a n d 13 f o r c.

Simplify.

Subtract 25 from each side.

Find the principal square ro o t o f each side.

3 cm

The side length b is 12 cm.

<£ Got It? 2. What is the side length a in the triangle at the right?

An if-then statement such as "If an animal is a horse, then it has four legs” is called a

conditional. Conditionals have two parts. The part following if is the hypothesis. The

part following then is the conclusion.

Li

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