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Pythagorean Theorem


Works for right angled triangles
Helps you to find an unknown side if you know two of the sides
The side across from the right angle is called the ‘hypotenuse’; it is always the
longest side. The other two sides are called the ‘legs’ of the triangle.
Pythagorean Theorem states a 2  b 2  c 2 where a and b are the legs and c is the
hypotenuse of the triangle.
To solve for the hypotenuse:
(Always draw an arrow from the right angle to the opposite side to show the
hypotenuse; the other two sides are interchangeable.)
a2  b2  c2
6.2 cm
Round final
answer to 1
decimal place
?
4.7 cm
Two more examples:
27.3 feet
14.7 m
6.3 m
x
y
34.2 feet
Note: Don’t skip steps in the solution; be sure to include units in the final
answer.
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Pythagorean Theorem Two
To find the side that is not the hypotenuse:
We still use a 2  b 2  c 2 , but can rearrange the equation to solve for the side we
want.
(Always draw an arrow from the right angle to the opposite side to show the
hypotenuse; the other two sides are interchangeable.)
?
8.6 cm
4.7 cm
Two more examples:
83.7 feet
x
6.3 m
14.7 m
142 feet
y
Note: Don’t skip steps in the solution; be sure to include units in the final
answer.
Pythagorean Theorem Three
How to solve a word problem:
1. Draw a diagram, labeling all the values you have been given.
2. Mark the right angle in the triangle. Draw an arrow to the hypotenuse.
3. Decide which version of the formula to use.
4. Solve for the missing side.
5. State the answer using words.
1. Jill is flying a kite and has let out 75 m of string. Jack is standing directly
below the kite and is 52.5 m from Jill. How high up is the kite?
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2. The foot of a 6-m ladder is placed 2 m from the base of a building. How
far up the building wall does the ladder reach?
3. A radio tower is supported by a guy wire. The tower is 12.5 m high and
the wire is anchored 5.4 m away. How long is the wire?
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Pythagorean Theorem Assignment
Due Date: __________________________
 Show complete solutions on loose-leaf.
 Draw a diagram for every question that does not have one.
1. Solve for the missing side:
a)
x
b)
5.0 feet
1.3 m
1.9 m
y
12.0 feet
c)
d)
11.2 mm
62.3”
z
w
51.8”
9.3 mm
2. The foot of a 3.6 m ladder is placed 1.1 m from the base of a building.
How far up the building wall does the ladder reach?
3. If the two diagonals of a field are the same length, the field has square
corners. How long is each diagonal in a field measuring 80 m by 70 m
with square corners?
4. A radio tower is 17 m high. Four wires are attached from the top of the
tower to points on the ground 15 m from the base of the tower. What is
the total length of the wires?
5. To find the width of a pond, a surveyor puts stakes at each end of the
lake and then locates a stake at C so that C is 90. How wide is the
pond?
A
B
135 m
95 m
C
6. What is the longest walking stick that can be placed in the bottom of a
trunk of length 80 cm and width 60 cm?
7. A boat leaves Halifax harbour and sails directly South for 25.6 km, then
sails East for 34.7 km. How far is the boat from the harbour?
8. Al is flying a kite and has let out 53 m of string. Sal is standing directly
below the kite and is 42 m from Al. How high up is the kite?
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