A right triangle is a triangle in which one angle measures 90 degrees. The longest side of the triangle, called the hypotenuse, is opposite the right angle. In a right triangle, the sides adjacent to the right angle are called legs and the angles opposite the legs are called the acute angles. In right triangle RST below altitude SV, the longest side is the hypotenuse, and the two shorter sides are the legs. The length of the hypotenuse is equal to the sum of the squares of the two legs.

## The Pythagorean Theorem

The Pythagorean theorem is a widely known mathematical theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. This equation can be written as a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. This theorem was discovered by the Greek mathematician Pythagoras in the 6th century BC and is still used today in mathematics and geometry.

## Analyzing Right Triangle RST

Using the Pythagorean theorem, we can analyze right triangle RST and calculate the length of each side. First, we must determine the lengths of the legs, a and b. Since we know that RST is a right triangle, we can use the Pythagorean theorem to calculate the length of the hypotenuse. If we know the lengths of the legs, we can calculate the length of the hypotenuse using the equation a2 + b2 = c2. Using this equation, we can calculate the length of the hypotenuse, which is equal to the length of the altitude SV.

## Applications of the Pythagorean Theorem

The Pythagorean theorem is used in a variety of fields, including architecture, engineering, and astronomy. In architecture, the Pythagorean theorem is used to calculate the length of the hypotenuse of a right triangle, which is used to determine the height of a building. In engineering, the theorem is used to calculate the length of a hypotenuse in a triangle, which is used to calculate the distance between two points. In astronomy, the theorem is used to calculate the distance between two celestial bodies.

## Conclusion

The Pythagorean theorem is an important mathematical theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. Using this theorem, we can analyze right triangle RST below altitude SV and calculate the length of each side. This theorem has many applications in architecture, engineering, and astronomy and is still used today.

In conclusion, the Pythagorean theorem is a widely used mathematical theorem which is used to calculate the length of the hypotenuse in a right triangle. Using this theorem, we can analyze right triangle RST below altitude SV and calculate the length of each side. This theorem has many applications in various fields and is still used today.