Geometry

# 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 1: If b = 4 and c = 3, find out the hypotenuse:

the length of the hypotenuse is 5

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

the length of the other cathetus is 12

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

the length of the diagonal is 26 cm

**Exercises**:

1) If one cathetus and the hypotenuse of a right triangle measure 8 and 10 cm, respectively, calculate the length of the other cathetus.

2) If a see a balloon at 500 m and it is 300 m over the ground. How long do I have to walk to be exactly under it?

Solutions: 1) 6 m ; 2) 400m

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