A right triangle is a type of triangle where one of the angles measures 90 degrees. This angle is called the right angle and is represented by a small square in the triangle's corner.
To solve a right triangle problem without knowing the bottom line, you can use the Pythagorean theorem, trigonometric ratios, or special right triangle properties. These methods involve using the known information about the triangle, such as the length of one side and the measures of the angles, to find the missing side lengths.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Trigonometric ratios, also known as trigonometric functions, are mathematical functions that relate the angles of a right triangle to the ratios of its sides. The three main trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These ratios can be used to find the missing side lengths of a right triangle when given one angle and one side length.
Special right triangle properties refer to the relationships between the sides and angles of right triangles with specific angle measures. These include the 45-45-90 triangle, where the two acute angles are both 45 degrees and the sides have a ratio of 1:1:√2, and the 30-60-90 triangle, where one acute angle is 30 degrees, the other is 60 degrees, and the sides have a ratio of 1:√3:2. These properties can be used to find the missing side lengths of these special right triangles.