In geometry, a theorem stating that in a right-angled triangle, the square of the
hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. If the hypotenuse is
h units long and the lengths of the other sides are
a and
b, then
h2 =
a2 +
b2.
The theorem provides a way of calculating the length of any side of a
right-angled triangle if the lengths of the other two sides are known. For example, to find the length of a bridge constructed over a valley 120 m wide, when the vertical drop of the bridge is 20 m:
Using Pythagoras' theorem
B2 = 1202 + 202, so
B2 = 14,400 + 400 = 14,800, giving
b = √14,800 = 121.66 (to two decimal places).
The length of the bridge is 121.66 m.
Pythagoras' theorem is also used to determine certain
trigonometric identities such as sin
2 θ + cos
2 θ = 1.
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