1. Basic Trigonometry
Sine
Cosine
Tangent

2.  The Language of Trig Opposite Hypotenuse target angle Adjacent
The target angle is either one of the acute angles of the right triangle.
Hypotenuse
Opposite
target angle 
Adjacent

3.  Trig Equations Hypotenuse Opposite target angle  Adjacent opposite
sin
Hypotenuse

4.  Trig Equations Hypotenuse Opposite target angle  Adjacent Adjacent
COS
Hypotenuse

5.  Trig Equations Hypotenuse Opposite target angle  Adjacent opposite
SOH - CAH - TOA

6. Given sides, find requested ratios:
Locate indicated angle and classify sides in relation to it.
Use proper equation and write the ratio.
Use calculator to round to the nearest ten-thousandths place.
Hypotenuse
Opposite
Adjacent
Find sin, cos, and tan of A.
8.2
opposite
sin A
24.5
Hypotenuse
23.1
COS A
Adjacent
Hypotenuse
24.5
8.2
opposite
TAN A
23.1
Adjacent

7. Given sides, find requested ratios:
Find sin A, cos A, tan A
Find sin B, cos B, tan B.
What do you notice?
Hypotenuse
Opposite
Adjacent
Opposite
Adjacent
6.8
opposite 4
opposite
sin A 
sin B 
7.5
Hypotenuse
7.5
Hypotenuse 4
COS A
6.8
Adjacent 
COS B
Adjacent 
7.5
Hypotenuse
Hypotenuse
7.5
6.8
opposite 4
TAN A 
opposite
TAN B  4
6.8
Adjacent
Adjacent

8. Solving for the unknown:
!!!!!! MAKE SURE YOUR CALCULATOR MODE IS SET TO DEGREES NOT RADIANS!!!!!!!!!
Unknown on top…..Multiply x
sin 40 24
Calculator: 24 * (sin 40) 
15.4

9. Solving for the unknown:
Unknown on bottom…..Divide 24
sin 40 x
Calculator: 24 (sin 40) 
37.3

10. Solving for the unknown:
Unknown angle…..use inverse
15.4 x
sin 24
Calculator: 2nd sin-1 (15.4/24) 
39.9

11. h h = 52.6(sin 30)  26.3 Solving problems using trig: 52.6 Hypotenuse
Choose your target angle and classify sides in relation to it.
Use proper function and write the equation placing the unknown wherever it falls.
Solve…Unless directed otherwise, round sides and angles to nearest tenth unless told otherwise.
Hypotenuse
Opposite
sin
Opposite
Hypotenuse h
sin 30 
52.6
h = 52.6(sin 30) 
26.3

12. x x = 6.1 (tan 41)  7.0 in Solving problems using trig: 6.1 Opposite
Adjacent
Opposite
Tan
Adjacent
6.1
Tan 41 x
x = 6.1 (tan 41) 
7.0 in

13. x x = 2nd COS (84/130)  50 Solving problems using trig: 84 130
Hypotenuse
Adjacent
Hypotenuse
cos
Adjacent x 84
cos
130
x = 2nd COS (84/130) 
50

14. Angle of Elevation The angle of elevation is always
Measured from the Horizontal UP…
It is usually INSIDE the triangle.

15. Angle of Depression x The angle of depression is always
Measured from the Horizontal DOWN…
It is usually OUTSIDE the triangle. x  
However….because horizontal lines are parallel, an angle of depression is equal to its alternate interior angle of elevation.

16. h = 30(tan 67) = 70.7m Practice h h opposite Opposite TAN 67 Adjacent

17. x  16 ft Adj Hyp Opp x ft x ft 32° 32° 25 ft 25 ft TAN
From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º. Find to the nearest foot, the height of the tree.
Adj
Hyp
Opp
TAN
x ft
x ft
32°
32°
x  16 ft
25 ft
25 ft

18. Example 2: From the top of a tower 60 feet high, the angle of depression to an object on the ground is 35. Find the distance from the object to the base of the tower to the nearest foot.
35°
60 ft
60 ft
TAN 35 x
35°
x  86 ft x

19. Example 3: In an isosceles triangle, the base is 28 cm long, and the legs are 17 cm long. Find the measure of a base angle to the nearest degree.
17 cm
28 cm x° 14
cos x
28/2=14 cm 17
x  35

20. Example 4: The height of a flagpole is 12 meters
Example 4: The height of a flagpole is 12 meters. A student stands 50 meters from the foot of the flagpole. What is the measure of the angle of elevation from the ground to the top of the flagpole to the nearest degree?
12 m
12 m
TAN x
50 m x°
x  13
50m