Pythagorean Theorem
In right angled-triangles, a special relationship exists between the squares of the two legs and
the square of the longest side called the hypotenuse.
leg
hypotenuse
leg
PYTHAGOREAN THEOREM
Finding the measure of the hypotenuse
Example 1: Solve for h.
Finding the length of one of the smaller sides
Example 2: Solve for x.
h 2  7 2  10 2
x 2  18 2  112
 49  100
 324  121
149
 203
h  149
x  203
 12.21
 14.25
Example 3: Two joggers run 8 miles north and then
5 miles west. What is the shortest distance, to the
nearest tenth of a mile, they must travel to return to
their starting point?
c 2  82  52
5m
 64  25
 89
8m
c2  a2  b2
Example 4: How far up a wall will an 11 m ladder
reach, if the foot of the ladder must be 4 m from the
base of the wall?
x 2  112  4 2
 121  16
105
c  89
x  105
 9.43
 10.25
They must travel 9.43 miles to return to their
starting point.
The ladder will reach 10.25 m up the wall.
NOTE:
1. If you are trying to find the size of the hypotenuse, add the squares of the two legs.
2
2
2
c  a b
2. If you are trying to find the size of one of the legs, subtract the square of the known leg from the
square of the hypotenuse.
2
2
2
b c a