Solving Right Triangles

A right triangle is a triangle that has one angle measuring 90 degrees.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

The hypotenuse is the longest side of a right triangle, opposite the right angle.

You can use sine, cosine, or tangent ratios to find the lengths of the sides. For example, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

You can calculate the missing angle using the fact that the sum of the angles in a triangle is 180 degrees. In a right triangle, the other two angles must sum to 90 degrees.

The larger the angle, the longer the side opposite that angle. Conversely, the smaller the angle, the shorter the side opposite that angle.

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.