1. Lesson Objectives
SWKOL how to use trigonometry to obtain values of sides and angles of right triangles

2. Trigonometry
Trigonometry relates the various sides and angles of right triangles
It is important to remember that all triangles have angles totaling 180°
Because a right triangle always has an angle of 90°, the other two angles must add up to 90° also

3. Angle Examples
What is the missing angle theta (q)?
56° q
34°

4. Angle Examples
What is the missing angle theta (q)?
72° q
18°

5. Trigonometry
Three functions in trigonometry relate the angles of a right triangle to its sides: sine, cosine, and tangent
By knowing how to use these functions, you can determine the value of any side of a right triangle when given the value of one side and angle

6. Trigonometry
There are three anagrams to remember the trigonometric functions
SOH: Sin(q) = opposite/hypotenuse
CAH: Cos(q) = adjacent/hypotenuse
TOA: Tan(q) = opposite/adjacent

7. Trigonometry The hypotenuse is the side opposite to the right angle
The opposite side is the side opposite to the angle theta (q)
The adjacent side is the side next to the angle theta (q) that is not the hypotenuse

8. Sides of a right triangle
hypotenuse
opposite
90o Θ
adjacent

9. Side Examples sin(60°) = 0.866 = x/15; x = 13
Use the trigonometric functions in your calculator to solve for the side X
60° 15
90o X
sin(60°) = = x/15; x = 13

10. Side Examples cos(45°) = 0.7071 = x/7.3; x = 5.2
Use the trigonometric functions in your calculator to solve for the side X
45°
7.3 X
90o
cos(45°) = = x/7.3; x = 5.2

11. Side Examples tan(30°) = 0.5774 = 53.7/x; x = 93.0
Use the trigonometric functions in your calculator to solve for the side X
53.7
90o
30° X
tan(30°) = = 53.7/x; x = 93.0

12. Trigonometry
You can also solve for the angles of a right triangle by using the same equations if you are given two of the sides

13. Angle Examples cos(q) = 32.2/64.4 = 0.500; q = 60°
Use the trigonometric functions in your calculator to solve for the angle q q
64.4
32.2
90o
cos(q) = 32.2/64.4 = 0.500; q = 60°

14. Angle Examples tan(q) = 8.7/5.0 = 1.7; q = 60°
Use the trigonometric functions in your calculator to solve for the angle q q
5.0
8.7
tan(q) = 8.7/5.0 = 1.7; q = 60°

15. Angle Examples sin(q) = 12.4/17.5 = 0.709; q = 45°
Use the trigonometric functions in your calculator to solve for the angle q
17.5
12.4 q
sin(q) = 12.4/17.5 = 0.709; q = 45°

16. Side Examples x= 17.0*cos40o =13.0 y=17.0*sin40o=10.9
Use the trigonometric functions in your calculator to solve for the sides x and y
17.0 y
40o x
x= 17.0*cos40o = y=17.0*sin40o=10.9

17. Trigonometry
The concepts that we discussed in this lesson will be important when we work with vectors.