The sinusoidal equation: a/sinA = b/sinB = c/sinC (use to find the missing page) sinA / a = sinB / b = sinC/c (use to find the missing angle) The cosine equation: a2 = b2 + c2 – 2bccos (A) (version given on the formula sheet to find the missing page) cos (A) = (b2 + c2 – a2) / 2bc (use this version to find a missing angle) Usually, if we have pairs of corresponding sides and angles, inside a side where a side or angle is unknown: SAA or SSA – Use the sinusoidal rule when a problem affects two sides and two angles When we need to determine angular measurements or side lengths in non-right triangles, we use the law of cosine and the sinusoidal law. The sinusoidal and consine rules apply to all triangles, you don`t necessarily need a right angle! Learn about the law of cosine, the sinusoidal distribution, and the ambiguous case of the sinusoidal distribution, and see functional examples by watching the video lesson: You can usually use the cosine rule if you get two sides and the closed angle (SAS) or if you get three sides and want to calculate an angle (SSS). To use the sinusoidal rule, you need to know two angles and one side (ASA) or two sides and one unclosed angle (SSA). Typically, we create an equation with two ratios provided and multiply by cross-referencing to isolate the unknown value. Whenever we get two sides and an angle and we look for another angle, we can use the law of sine. However, we need to be aware of the possibilities that could arise from the relationships between the given measures. Sometimes the relationship between the sides and an angle does not even result in a triangle. In other cases, they can lead to two possible triangles, and we have to consider both situations. This is called the ambiguous case of the law of the sine.
When solving an angle, the formula must be rearranged, and the last step is always to take the reverse gear to get the angle measurement. Below is a diagram of the possible outcomes based on the measures given:.