The Pythagorean Theorem

In a right-angled triangle, the side opposite the right angle is called the hypotenuse. The two sides that form the right angle are called catheti or legs.

Pythagorean Theorem: in a right triangle, the addition of the squares of the lengths of the catheti equals the square of the length of the hypotenuse.

Example 2: If a = 13 and c = 5, find out the other cathetus.

 

Example 3: Which is the length of the diagonal of a rectangle with base 24 cm and height 10cm?

  

 

 

Exercises:

1.- Could a right triangle have side lengths of 29, 21, and 20 inches?

2.- A boat sails east for 20 km and then it sails north for 5 km. How far is the boat from its starting position?

Solutions: 1.- Yes; 2.- 20.6 km