2. Solve the triangle below. Round answers to nearest tenth.

3. Objective: To understand and apply the SINE ratio.

4. We need to do some housekeeping before we can proceed…

5. In trigonometry, the ratio we are talking about is the comparison of the sides of a RIGHT TRIANGLE. Two things MUST BE understood: 1. This is the hypotenuse.. This will ALWAYS be the hypotenuse 2. This is 90°… this makes the right triangle a right triangle…. Without it, we can not do this trig.

6. Remember we won’t use the right angle X

7. θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’. Don’t let it scare you… it’s like ‘x’ except for angle measure. One more thing…

8. Here we go!!!!

9. Definition of Sine Ratio.Sine Ratio  For any right triangle Sin  = Opposite side hypotenuse

10. Try This  Write the Sine ratios for < K and < J J L K 6 8 10 Sin K = Sin J = 8 10 6

11. Example: Find the value of x. Step 1: Mark the “Angle of Perspective”. Step 2: Label the sides (Hyp / Opp). Step 3: Select a trigonometry ratio (sin/tan). Sin = Step 4: Substitute the values into the equation. Sin 25 = Step 5: Solve the equation : Change Sin 25 into a decimal. Cross multiply and solve. Angle of Perspective Hyp opp x = (0.4226) (12) x = 5.07 cm =

12. Problem 1 11 In the figure, find y Sin35  = Opposite Side hypotenuse y 11 y = 6.31 35° y Sin35  = y = 11 sin35 

13. Problem 2 Find the missing side. Round to the nearest tenth. 283 m x

14. Problem 3:  Find the height and length of the base of the ramp shown.