Trigonometry Study Sheet Start with a Triangle Ask: What kind of triangle is it? (only 2 options) Right triangle Non-right triangle Now ask: are any other angles given or needed? No? Pythagorean Theorem a2 + b2= c2 Yes? SOH CAH TOA Now ask: is there a known angle opposite a known side? Yes? Sine Law No? Cosine Law So, do you know what to use and how to use it? What are the steps? Steps for SOH CAH TOA for sides: 1. Label sides hyp, opp, adj (opp is the side opposite the angle given or needed) Sine Law for sides We know angle C = 37º, a = 8 and b = 11 The Law of Cosines says: c2 = a2 + b2 - 2ab cos(C) Put in the values we know: Do the 1st & 2nd “chunk”: 2. Decide SOH, CAH or TOA equation by circling what is needed and what is given (eliminate the equations that have a side that is not circled) 3. Fill in what is known in your equation, put the sinA, cosA or tanA over 1 then do cross multiply and divide 4. Don't forget units! SOH CAH TOA for angles Cosine Law for sides Example: How long is side "c" ... ? Subtract: Take the square root: x = sin (42) × 11 ÷ 𝑠𝑖𝑛50 = 9.6 units Sine Law for angles c2 = 82 + 112 - 2 × 8 × 11 × cos(37º) c2 = 185 - 140.448… c2 = 44.44... c = √44.44 = 6.67 (to 2 decimal places) Answer: c = 6.67 units Cosine Law for angles Example: What is Angle "C" ...? In this triangle we know the three sides: a = 8, b = 6 and c = 7. Use The Law of Cosines (angle version) to find angle C : Make sure “C” and “c” are the angle and side opposite each other cos C = (a² + b² - c²)/2ab = (8² + 6² - 7²)/(2×8×6) do the top, then do the bottom = 51/96 = 0.53125 C = cos-1(0.53125) = 57.9° correct to one decimal place.