the pythagorean theorem states a relationship between the sides of a right triangle. A right triangle has one 90 degree angle. The hypotenuse of a right triangle is theside opposite the degree angle , and it is the longest side.

if the length of the hypotenuse of a right triangle is unknow, the following formula can be used to solve for it:

hypotenuse=square root (leg)2 (leg)2

if the length of one side (leg) of a right triangle is unknown, the following formula can be used to solve for it:

leg= square root (hypotenuse)2- (leg)2

1.find the length of a ramp that is 8 feet long and 6 feet high.


an l-shaped sidewalk from a parking lot to a fountain is shown in the figure below. The distance directly across the grass to the fountaion is 650 feet. The distance to the corner is 600 feet. Find the distance from the corner of the fountain.

You've noted that the length of the hypotenuse is \sqrt{ Leg1 ^2 + Leg2 ^2}. For (1), you're told that Leg1 = 8 and Leg2 = 6, so what's the length of the hypotenuse?

For (2) you have Leg2 = \sqrt {Hyp^2 - Leg1^2}. Plug and chug.

question 1: The 8 foot ramp is the hypotenuse of the triangle, the height of the other side of the triangle is 6', therefore...

8 squared equals the sum of: 6 squared plus the base squared.
Since 8 squared = 64, and the sum of 6 squared = 36 plus the base squared!
Transpose the theorem: subtract 6 squared (36) from 8 squared (64)= base squared.
Thus (64-36)= 28= the square of the base.

The square root of the base 5.25... feet.
The sidewalk question doesn't have a diagram, but just plug in different values in
the formula above.

1. a^2 + b^2= c^2
2. 8^2 + 6^2= c^2
3.(8*8=64) + (6*6=36)= c^2
4. 64-36=28
5. c=28
the square base is 28