1. Trigonometry
Students will be able to use right triangle trig to solve everyday problems.
Students will use sine, cosine, tangent and inverse trig functions to solve for missing side and angle measurements.

2. Triangle Review What do you remember Types Names Properties
What lengths make a triangle
How do we determine type
How are sides and angles related

3. Did you remember
3 Sides Angles add to 180 Right, Acute, Obtuse, Scalene, Isosceles, Equilateral Sum of shorter 2 sides must be greater than longest Longest side across from largest angle, smallest and smallest

4. Examples
Can these lengths make a triangle, is yes what kind? 6,10,8 5,7,10 9,16,8 What type of triangle is the following?

5. More Example
Put the angle in order from largest to smallest Put the sides in order from longest to shortest

6. Homework
Worksheet on these properties

7. Trigonometry
Can only be used with right triangles W will use it to find measures of missing sides and angles All angles in right triangles are ratios of two of the sides All similar triangles corresponding angles will have the same trig ratio

8. Describing the Sides in relation to a right triangle
Opposite side in relationship to angle using
Across from the angle, does not touch the angle we are using
Adjacent side in relationship to angle using
Touches the angle, not hypotenuse, connects angle to right angle
Hypotenuse
Always the longest side, across from the right angle

9. Trig Ratios and Right Triangles
The sides of the triangle have names, but it depends on the angle you are looking from. From angle A – Blue From angle B – Red

10. Trig Ratios
The trigonometric value of an angle is related to a specific ratio of two of the sides of the triangle
SOH
CAH
TOA

11. Setting Up Trig Ratio
You should be able to set up all 3 trig ratios from all the angles in a triangle Make sure you have correct angle and correct sides

12. Examples Continued

13. Homework
Wkst on setting up trig ratios

14. Finding Missing Sides
To find the missing side of a triangle you need to set up a specific trig ratio based on angle given and side you want to find These will look similar to proportions

15. Set up Determine Trig ratio you are using
What angle is given
What side is given
What side do you need to find
Which trig ration does this match up with
Set up trig ratio – using what you determined about, there should be only 1 unknown, this is the work I need to see
Solve trig ratio – you need a calculator with the trig functions to do this
What are some things you noticed when solving

16. Calculator
Make sure your calculator is set up in correctly Mode Degree Sides lengths should always be rounded to the nearest hundredth unless specified otherwise

17. Examples

18. Your work fro trig ratios is the set up of the trig ratio, everything else is done in your calculator Do you notice when you multiple or divide

19. Homework
Worksheet on 3 trig rations Make sure you show set up and label your answers

20. Solving for Angles
We can also use trig ratios to calculate angles measure in a triangle
Similar idea to how we did sides for triangles
What angle are we solving for
What sides do we have in relationship to the angle
What trig ratio uses those sides
Substitute and solve, round to nearest degree

21. Using calculator

22. Examples

23. Homework
Worksheet Trig ratios finding angle measures Remember to round to the nearest degree for your lable

24. Word Problems

25. Problem Solving
Angle of Depression – angle line forms with horizon, coming down Angle of Elevation – angle formed with horizon going up

26. Example Continued
When an 18 ft ladder is leaning against a wall and it makes a 68 degree angle with the ground. How high up the wall does the ladder reach?

28. Homework
Due 4/10 or 4/11 depending on class Pg even Pg odd 10,11,12 Honors Magic Square pg 607 Due 4/14 4/15 depending on class