Non-Right Triangle Trigonometry

Non-right triangle trigonometry is the branch of trigonometry that deals with calculating angles and sides of triangles that are not right triangles. In a non-right triangle, all three angles are different from 90 degrees. To calculate angles in a non-right triangle using trigonometry, you can use the Law of Sines or the Law of Cosines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. For example, if you have a triangle with side lengths of 5, 7, and 9, and you want to find the measure of one of the angles, you can use the Law of Cosines to calculate it. Let’s say you want to find the measure of angle A, opposite side length 9. Using the Law of Cosines: (9^2 = 5^2 + 7^2 – 2(5)(7)cos(A)) (81 = 25 + 49 – 70cos(A)) (81 = 74 – 70cos(A)) (7 = -70cos(A)) (cos(A) = -frac{1}{10}) (A ≈ 99.6°) A fact that can be verified is that in any triangle, the sum of all three interior angles will always add up to 180 degrees. This fact can be helpful when calculating angles in non-right triangles using trigonometry.