1. Agenda 1) Bell Work / Homework Check 2) Outcomes 3) Pop Quiz 4) Notes 9.5 - Trig Ratio

2. Outcomes I will be able to: 1) Use properties of Special Right Triangles to find missing lengths. 2) Understand trigonometric ratios in right triangles. 3) Solve for missing lengths using trigonometric ratios.

3. BellWork Solve for the variable using the Right Triangle Geometric Mean Theorems.

4. 9.5 Trigonometric Ratios Trigonometric Ratio: ____________________________. The word “trigonometry” is derived from the ancient Greek language and means ___________________. Is a ratio of the lengths of two sides of a right triangle. measurement of triangles

5. 9.5 Trig Ratios ***Pretend you are standing at angle A

6. 9.5 Trig Ratios Pneumonic Device: If you remember the word SOHCAHTOA, you can remember the trig ratios. SOHCAHTOA stands for: S = Sine O = Opposite / H = Hypotenuse C = CosineA = Adjacent / H = Hypotenuse T = TangentO = Opposite / A = Adjacent

7. Examples Sin A = Sin D = Cos A =Cos D = Tan A =Tan D = How do these ratios compare? Are these triangles similar? Why/Why not?

8. Examples 2. Find the sine, cosine and tangent of a 45°-45°-90°. Sin A = Cos A = Tan A = = 1 What do we know about all 45-45-90 right triangles? They are similar Note: Since all 45°-45°-90° triangles are similar, you can simplify any problem involving trig ratios of a 45°- 45°-90° to the ratios above. A B C

9. Examples 3. Find the sine, cosine and tangent of A in a 30°-60°-90° Sin A = Cos A = Tan A = *All 30°-60°-90° are similar so they will have these same ratios.

10. Examples 4) Use a calculator or your chart to find the following to 4 decimal places: **Note your calculator must be in degree mode. **Most tablet calculator do not work for these. a) sin 56° = b) cos 84° = c) tan 16° = *Note you must be able to convert the trig ratio to a decimal to be able to solve for pieces in the triangle later on..8290.1045.2867

11. Examples 5) Will sine and cosine ever be greater than 1? No Why? Because the legs of a right triangle can never be longer than the hypotenuse. So you are always dividing them by something bigger than what they are. Will tangent ever be greater than 1? Yes, because one leg can be greater than the other.

12. Angle of Elevation Angle of Elevation: When you stand and look up at a point in the distance, the angle that your line of sight makes with a line drawn horizontally Where is the angle of elevation? Angle of elevation

13. Examples 1. The angle of elevation from the base to the top of a playground slide is 55°. The slide takes up 10 feet of space horizontally along the ground. Estimate the height and length of the slide. 1) Draw Picture: 2) Determine what piece you have 3) Create trig ratios Cos 55 = Tan 55 = opp adj hyp 4) Convert trig ratio to decimal 5) Solve for variable Y = 17.43 ft X = 14.28 ft

14. Examples 2. You are measuring the height of a tower. You stand 154 feet from the base of the tower and measure the angle of elevation from a point on the ground to the top of the tower to be 38°. Estimate the height of the tower. Which trig ratio do we use? Tan 38 = Solve for the variable x = 120.3 ft.

15. Examples 3. You stand at the top of a soapbox derby hill and look downwards. The angle of depression is the angle between your line of sight and a line drawn horizontally. The difference between the elevations at the top and bottom of the hill is called the vertical drop. If the vertical drop is 50 feet and the angle of depression is 13°, find the distance d that a soapbox would travel on this hill. Picture: What trig ratio do we have? Solve for the variable x = 222.3 ft.