1. Sine Law: The ratio of two sides of an acute triangle is equal to the ratio of the sines of the angles, opposite those sides. To use the sine law you need at least 1 unknown and 3 knowns. For example: one opposite angle-side pair along with one other value.
2. Laws
2.1. Cosine Law: This law is used primarily in two situations: when two sides and their included angle are given, and when three sides are given. Formula: a 2 = b 2 + c 2 -2bc cos(A)
3. Triangles
3.1. • Similar Triangles Similar figures have the same angles but have different side lengths. They share a common ratio/scale factor.
3.2. • Acute triangles The longest side of an acute triangle is opposite the largest angle. Similarly, the shortest side of an acute triangle is opposite the smallest angle.
3.3. • Congruent triangles Congruent figures have the same angles and side lengths.
4. Formulas
4.1. • Soh Cah Toa To help you remember what sides are involved with each ratio, we use this acronym, SOH CAH TOA, as a mnemonic device. S:O/H C:A/H T:O/A Note: As long as you have 2 pieces of information in a right triangle (along with the right angle), you can find ALL other measurements!
4.2. • Tangent Ratio The tangent ratio is a comparison of the sides of a triangle, and is specific to one of the acute angles. The tangent ratio is the ratio of the side "opposite" the specified angle, with the side "adjacent" to the specified angle.
4.3. • Sine and Cosine Ratios Sine is the ratio of the opposite side of an angle and the hypotenuse. Cosine is the ratio of the adjacent side of an angle and the hypotenuse.
