The Pythagorean Theorem must work in any 90 degree triangle. This means that if you know two of the sides, you can always find the third one.
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In the right triangle at the left, we know that:
h2 = 62 + 82
Simplifying the squares gives:
h2 = 36 + 64
and then:
h2 = 100
h = 10
(by doing the square root of 100)
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Here's another one:
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In this example, the missing side is not the long one. But the theorem still works,as long as you start with the hypotenuse:
152 = x2 + 92
Simplifying the squares gives:
225 = x2 + 81
and then:
225 - 81 = x2
144 = x2
12 = x
(Notice that we had to rearrange the equation)
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Now something different will happen:
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In the right triangle at the left, we know that:
h2 = 72 + 102
Simplifying the squares gives:
h2 = 49 + 100
h2 = 149
This square root is not perfect. A calculator gives:
h = 12.2
(rounded to one decimal place)
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And one more example:
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Again, the missing side is not the long one. But we start with the hypotenuse:
182 = x2 + 112
Simplifying the squares gives:
324 = x2 + 121
and then:
324 - 121 = x2
203 = x2
14.2 = x
(We had to rearrange the equation, and round the answer.)
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Here's a real problem that uses the theorem:
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How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall?
112 = x2 + 42
121 = x2 + 16
121 - 16 = x2
105 = x2
10.2 = x
The ladder will reach 10.2 metres up the wall.
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Now you're ready for the QUIZ!
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