The Pythagorean Theorem

1
The Pythagorean Theorem
a2 b2 c2
OR
a2 c2 b2
Which side is the hypotenuse?
The right angle points to the hypotenuse. Its
the side labelled c.
2
When calculating the hypotenuse, we add the area
of the squares of the other two sides.
Calculate side c.
c2 a2 b2
c2 82 62
c2 64 36
c2 100
c 10
3
Calculate the length of side x.
b2 c2 a2
x2 122 72
a
b
x2 144 49
x2 95
c
When calculating a side, we determine the
difference of the area of the square of the
hypotenuse and the area of the square of the
known side.
x 9.7
4
The length and width of a rectangle are 12 cm and
15 cm. Calculate the length of the diagonal.
c2 a2 b2
d 2 152 122
d
d 2 225 144
d 2 369
d 19.2 cm
5
Tanya is making a party hat using a cone made out
of paper. Determine the height of the cone.
b2 c2 a2
h2 132 52
h2 169 25
h2 144
h 12 cm