Right Triangle Trigonometry

Right Triangle Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of a right triangle. In a right triangle, one angle is always 90 degrees. Trigonometry involves using the sine, cosine, and tangent functions to calculate the unknown sides or angles of a right triangle. These functions are defined as follows: – Sine (sin): opposite/hypotenuse – Cosine (cos): adjacent/hypotenuse – Tangent (tan): opposite/adjacent To calculate an angle in a right triangle using trigonometry, you can use one of the trigonometric ratios mentioned above. For example, if you know the length of the opposite side and the hypotenuse, you can use the sine function to find the angle: sin(angle) = opposite/hypotenuse Similarly, if you know the length of the adjacent side and the hypotenuse, you can use the cosine function to find the angle: cos(angle) = adjacent/hypotenuse And if you know the length of the opposite side and the adjacent side, you can use the tangent function to find the angle: tan(angle) = opposite/adjacent For example, if you have a right triangle with an opposite side of 5 units and a hypotenuse of 13 units, you can use the sine function to find the angle: sin(angle) = 5/13 angle = sin^(-1) (5/13) angle ≈ 22.6 degrees A key fact to remember is that the sum of the angles in a triangle is always 180 degrees. Therefore, once you find one angle using trigonometry, you can calculate the other angles by subtracting the known angles from 180 degrees. Overall, Right Triangle Trigonometry is a useful tool for solving problems involving right triangles and calculating unknown angles or sides based on given information.