One of the most famous mathematicians who has ever lived, Pythagoras, a Greek scholar who lived way back in the 6th century B.C. (back when Bob Dole was learning geometry), came up with one of the most famous theorems ever, the Pythagorean Theorem. It says - in a right triangle, the square of the measure of the hypotenuse equals the sum of the squares of the measures of the two legs. This theorem is normally represented by the following equation: a2 + b2 = c2, where c represents the hypotenuse.
With this theorem, if you are given the measures of two sides of a triangle, you can easily find the measure of the other side.
Example
1. Problem: Find the value of c.
Accompanying Figure
Solution: a2 + b2 = c2 Write the Pythagorean
Theorem and then plug in any
given information.
52 + 122 = c2 The information that was
given in the figure was
plugged in.
169 = c2 Solve for c By finding the square root of the number
c = 13
2. Problem: A ladder 12 meters long leans
against a building. It rests on
the wall at a point 10 meters
above the ground. Find the angle
the ladder makes with the ground.
Solution: Make sure you know what is being
asked. Then use the given
information to draw and label a
figure.
a2+b2=c
12,2+10,2=c
c2=144+100
c=244
square root of 244 is 15.62
c=15.62
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