Ch. 3-2 & 3-3 The Pythagorean Theorem
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Ch. 3-2 & 3-3 The Pythagorean Theorem
Hypotenuse
a
c
Leg
-The Pythagorean Theorem is
an equation that shows the
relationship between
hypotenuse and legs of right
triangles.
a2 + b2 = c2 where a and b are
the legs and c is the
hypotenuse
Must be a right triangle
Leg b
-You use the Pythagorean theorem to find a missing
leg or hypotenuse of a right triangle.
Example 1: Find the length of the hypotenuse of the right triangles below.
a.)
b.)
Plug into the formula
52 + 122 = c2
5 cm.
c
12 cm.
25 + 144 =
c2
c = 169  13 cm
c
12
24
Plug into the formula
242 + 122 = c2
576 + 144 = c2
c=
720  27
Example 2: Find the length of the missing legs below.
a.)
b
9 cm
15 cm
Formula:
c2 - a2 = b2
Round to nearest one
Plug into the formula 152 - 92 = b2
225 - 81 = b2
b2 = 144
Take the square root on both sides
b = 12 cm
Formula:
c2 - a2 = b2
Round to nearest tenth
Plug into the formula 182 - 52 = a2
324 - 25 = a2
a2 = 299
b.)
18 cm
a
Take the square root on both sides
a = 17.3 cm
5 cm
Example 3: Draw each situation below to figure out if you are solving for a
leg or a hypotenuse. Then solve the problem
a.) A 10 ft. long slide is attached to a deck that is 5 ft. high. Find the
distance from the bottom of the deck to the bottom of the slide to the
nearest tenth.
8.7 ft.
10
5
?
b.) A ramp is 1 ft. high. The base of the ramp extends 14 ft. along the side
of a building. How long is the sloped part of the ramp to the nearest
hundredth of a foot.?
??
1
14.04 ft.
?
Pythagorean Theorem used in roofing!
Homework
• Pg. 114
Pg. 120
2-20 even &
2-18 even
• Ec pg 608 5-16all round to nearest whole
number.