Pythagoras Theorem

The theorem

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides:

a^2 + b^2 = c^2

where $c$ is the hypotenuse and $a$ , $b$ are the two shorter sides.

Worked example

In a rectangular park that is 60 meters by 91 meters, a dog began in the northwest corner and ran south along the length of the park. Then the dog ran east along the width to the southeast corner. Finally, the dog ran back to the northwest corner. How far did the dog run in total?

Solution: The first two legs of the run are the two sides of the rectangle, 60 m and 91 m. The final leg, straight back to the start, is the diagonal of the rectangle, the hypotenuse of a right triangle with legs 60 and 91:

c = \sqrt{60^2 + 91^2} = \sqrt{3600 + 8281} = \sqrt{11881} = 109 \text{ m}

Total distance run: $60 + 91 + 109 = 260$ meters.

Pythagoras Theorem

The theorem

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides:

a^2 + b^2 = c^2

where $c$ is the hypotenuse and $a$ , $b$ are the two shorter sides.

Worked example

c = \sqrt{60^2 + 91^2} = \sqrt{3600 + 8281} = \sqrt{11881} = 109 \text{ m}

Total distance run: $60 + 91 + 109 = 260$ meters.

Pythagoras Theorem

The theorem

Worked example

Continue learning

Pythagoras Theorem

The theorem

Worked example

Continue learning