501 Geometry Questions

Example 3: Find CD.

a^2 + b^2 = c^2

202 + b^2 = 40^2

400 + b^2 = 1,600

b^2 = 1,200

Take the square root of each side:

b^2 = 1,200

b= 20 3 

Additional Application of Pythagorean Theorems

The Pythagorean theorem can only find a side of a right triangle. However,
if all the sides of any given triangle are known, but none of the angles are
known, the Pythagorean theorem can tell you whether that triangle is
obtuse or acute.
If the square of the longest side is largerthan the sum of the squares of
two smaller sides, then the longest side is creating an obtuseangle between
the two smaller sides and the triangle is obtuse. Conversely, if the square of
the longest side is smallerthan the sum of the squares of two smaller sides,
then the longest side creates an acuteangle between the two smaller sides
and the triangle is acute.

Caution!Before using the Pythagorean theorem to determine if triangles
are acute or obtuse in the following two examples, remember this impor-
tant rule about the sides of triangles: the sum of any two sides of a triangle
must be longer than the third side, or else the triangle cannot exist.

a = 20

E

C

D

b =?

c = 40

501 Geometry Questions