Right Triangle Trigonometry

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 08:55 PM UTC

Here we will discuss all the aspects of trigonometry in a right triangle along with its applications in triangles and circles.

1. Right Triangle Trig

2. p
Remember…. Hy Opp
Reciprocals!
Adj
opp hyp
sin   csc  
hyp opp
adj hyp
cos   sec  
hyp adj
opp
tan   adj
adj cot  
opp
*Opposite and adjacent will change according to which
angle you are using!

3. Find all 6 trig
a 2  b 2 c 2 13
12
2 2 2
a  12 13
a 2  144 169

2
a
a 25
a 5

4. Find all 6 trig
2 13
a 2  b 2 c 2 4
62  42 c 2
36  16 c 2

c 2 52 6
c  4 13
c 2 13
13
2 13
2
13
3 13 13
13 3
2 3
3 2

5. Find all 6 Trig Values. sin  
3
x 2  32 52 5
5
x 2  9 25 3
x 2 16 
4
x 4
3 5
5 3
4 5
5 4
3 4
4 3

6. 2
Find all 6 Trig Values. tan  
2 2 2
6 2 10
6  2 h
2
2
36  4 h

h 2 40 6
h 2 10
10 10
10
3 10 10
10 3
1 3
3

7. Find all 6 Trig Values. sec  
8
5
52  b 2 82 8
25  b 2 64 39

h 39 5
h  39
39 8 39
8 39
5 8
8 5
39 5 39
5 39

8. Find x. (3 Decimals)
x 4
4 sin 38 

38°
x
4
x
sin 38
x 6.497

9. Find x. (2 Decimals)
x
27° cos 27 

10 x 10
x 10 cos 27 
x 8.91

10. Find x. (2 Decimals)
x
cos 64 

6 6
64°
x
x 6 cos 64 
x 2.63

11. Find x. (2 Decimals)
15
tan 46 

46° x
x
15
x
15
tan 46 
x 14.49

12. Find x. (2 Decimals)
x
tan 53 

x
23
53°
23 x 23 tan 53
x 30.52

13. To find a missing angle:
 Type 2nd (Trig Function) then x/y
8
sin  
15
Make sure that your
Calculators are set
On DEGREES!

14. Find x.
22
55
22 sin x 

x° 55
 1 22
x sin

55
x 23.58 

15. Right Triangle Word
Problems

16. Angle of Elevation
 Angle from the horizontal up

17. Angle of Depression
 Angle from the horizontal down

18. A guy wire is 3.5 feet from a pole and the pole is
12 feet high. What is the angle of elevation?

19. A 16 foot ladder is leaning against a wall and
makes an angle of 36° with the ground. How
high up does the ladder reach?

20. The angle of depression from a lighthouse to a
boat is 29°. If the lighthouse is 40 foot
tall, how far way from the shore is the

21. The sun is making a tree’s shadow 16 feet long. If
the tree is 8 feet high, what is the angle of
depression from the sun?

22. A golfer is standing at the tee, looking up to the
green on a hill. If the tee is 36 yards lower than
the green and the angle of elevation from the tee
to the hole is 12°, find the distance from the tee to
the hole.

23. A ramp for unloading a moving truck has an angle
of elevation of 32°. If the top of the ramp is 4 feet
above the ground, estimate the length of the

24. A falcon at a height of 200 feet sees two mice (A &
B). The angle of depression to mice A is 18° and
the angle of depression to mice B is 28°. Find the
distance between the two mice.

25. Arc Length and Sector
Area
Linear and Angular Speed

26. Arc Length Formula

27.

28.

29.

30.

31.

32. Sector Area Formula

33. Given a circle of radius 4, find the area
of a sector subtended by the arc.

34. Given a circle of radius 4, find the area
of a sector subtended by the arc.

35. Given a circle of radius 6, find the area
of a sector subtended by the arc.

36. Given a circle of radius 6, find the area
of a sector subtended by the arc.

37. Given a circle of radius 6, find the area
of a sector subtended by the arc.
3.78

38. Given a circle of radius 6, find the area
of a sector subtended by the arc.
6.03

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