2. Chapter : Trigonometry Lesson 3: Finding the Angles

3. REMEMBER… The total angles of a triangle always add up to = 180° You must know how to LABEL your triangle…

4. Solving for UNKNOWN ANGLES #1. Label your triangle’s hypotenuse. #2. Label your triangle’s opposite and adjacent sides depending on which angle you are interested in solving. #3. Choose the appropriate formula depending on which side you know and the side you want to solve for. #4. Write down the formula, insert the values, and find your ratio by dividing. #5. Find the inverse of the function using your calculator.

5. Solving for angle A using Sine A 4.00 cm Opposite to <A. Hypotenuse 7.21 cm Tip: We know we will eventually have to use the second function on our calculators to get the angle. We know all three sides so we can use any formula. All three have a different ratio but they will give the same angle. =.5548 RATIO sin -1.5548 = 33.7° Inverse sin to get < sin A = opp hyp = 4.00 7.21

6. Solving for angle A using Cosine A 6.00 cm Adjacent to <A Hypotenuse 7.21 cm Tip: We know we will have eventually have to use the second function on our calculators to get the angle. We know all three sides so we can use any formula. All three have a different ratio but they will give the same angle. =.8322 RATIO cos -1.8322 = 33.7° Inverse cos to get < cos A = adj hyp = 6.00 7.21

7. Solving for angle A using Tangent A 4.00 cm Opposite to <A. 6.00 cm Adjacent to <A Tip: We know we will have eventually have to use the second function on our calculators to get the angle. We know all three sides so we can use any formula. All three have a different ratio but they will give the same angle. =.6667 RATIO tan -1.6667 = 33.7° Inverse tan to get < tan A = opp adj = 4.00 6.00

8. Summary Trig FunctionRatioAngle SINE.5548 COSINE.8322 TANGENT.6667 Different RatiosSame Angles