The Pythagorean theorem is a fundamental formula used to find the length of one side of a right triangle if the other two sides are known. It is expressed as:
a² + b² = c²
where:
- a and b are the lengths of the legs (the two sides that form the right angle),
- c is the length of the hypotenuse (the side opposite the right angle).
In your case, you have two legs measuring 8 km and 5 km, and you want to find C (the hypotenuse).
Step-by-step solution:
- Square both known side lengths:
- 8 km squared is 8 × 8 = 64 km²
- 5 km squared is 5 × 5 = 25 km²
- Add those squares: 64 + 25 = 89 km²
- Find the square root of the sum to get C:
C = √89 ≈ 9.43 km
Therefore, the length of side C is approximately 9.43 kilometers.