1. 6.2 Trigonometry of Right Triangles
Deuteronomy 31:6 Be strong and courageous. Do not be afraid
or terrified because of them, for the LORD your God goes with
you; he will never leave you nor forsake you.

2. SOH CAH TOA

3. SOH CAH TOA

4. SOH CAH TOA
opposite
Sin θ =
hypotenuse

5. SOH CAH TOA
opposite
Sin θ =
hypotenuse
adjacent
Cos θ =
hypotenuse

6. SOH CAH TOA
opposite
Sin θ =
hypotenuse
adjacent
Cos θ =
hypotenuse
opposite
Tan θ =
adjacent

7. 3
If tan θ = and θ is in QIII, find all the trig values.
2

8. 3
If tan θ = and θ is in QIII, find all the trig values.
2

9. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c

10. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c
−3 −3 13
sin θ = =
13 13

11. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c
−3 −3 13
sin θ = =
13 13
−2 −2 13
cosθ = =
13 13

12. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c
−3 −3 13
sin θ = =
13 13
−2 −2 13
cosθ = =
13 13
3
tan θ =
2

13. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c
−3 −3 13 − 13
sin θ = = cscθ =
13 13 3
−2 −2 13
cosθ = =
13 13
3
tan θ =
2

14. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c
−3 −3 13 − 13
sin θ = = cscθ =
13 13 3
−2 −2 13 − 13
cosθ = = secθ =
13 13 2
3
tan θ =
2

15. 3
If tan θ = and θ is in QIII, find all the trig values.
2
2 2 2
( −3) + ( −2 ) =c
2
9+4 = c
13 = c
−3 −3 13 − 13
sin θ = = cscθ =
13 13 3
−2 −2 13 − 13
cosθ = = secθ =
13 13 2
3 2
tan θ = cot θ =
2 3

16. Review from Geometry - Special Right Triangles

17. Review from Geometry - Special Right Triangles
60°
45°
1 1
2 1
2 2
45° 30°
2 3
2 2

18. Review from Geometry - Special Right Triangles
60°
45°
1 1
2 1
2 2
45° 30°
2 3
2 2
Look at the sin, cos and tan of these angles to see the
connection of these triangles to the Unit Circle

19. Review from Geometry - Pythagorean Triples

20. Review from Geometry - Pythagorean Triples
c 2 2
a +b = c 2
a
b

21. Review from Geometry - Pythagorean Triples
c 2 2
a +b = c 2
a
b
3, 4, 5 and it ' s dilations

22. Review from Geometry - Pythagorean Triples
c 2 2
a +b = c 2
a
b
3, 4, 5 and it ' s dilations
5, 12, 13 and it ' s dilations

23. Review from Geometry - Pythagorean Triples
c 2 2
a +b = c 2
a
b
3, 4, 5 and it ' s dilations
5, 12, 13 and it ' s dilations
7, 24, 25 and it ' s dilations

24. Review from Geometry
Angles of Elevation & Depression

25. Review from Geometry
Angles of Elevation & Depression

26. Review from Geometry
Angles of Elevation & Depression

27. Review from Geometry
Angles of Elevation & Depression
If the lines are parallel,
then the alternate interior angles are congruent.

28. Review from Geometry
Angles of Elevation & Depression
If the lines are parallel,
then the alternate interior angles are congruent.
∴ angle of depression = angle of elevation

29. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.

30. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.
h=b−a

31. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.
a
tan 21° =
700
h=b−a

32. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.
a
tan 21° =
700
a = 700 tan 21° ≈ 268.7
h=b−a

33. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.
a
tan 21° =
700
a = 700 tan 21° ≈ 268.7
b
tan 23° =
700
h=b−a

34. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.
a
tan 21° =
700
a = 700 tan 21° ≈ 268.7
b
tan 23° =
700
b = 700 tan 23° ≈ 297.1
h=b−a

35. From a point 700 feet from the base of a building, it is
observed that the angle of elevation to the top of the
building is 21 degrees and the angle of elevation to the
top of a flagpole atop the building is 23 degrees. Find
the height of the flagpole.
a
tan 21° =
700
a = 700 tan 21° ≈ 268.7
b
tan 23° =
700
b = 700 tan 23° ≈ 297.1
h=b−a h ≈ 297.1− 268.7 ≈ 28.4 feet

36. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)

37. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.

38. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.
β
130
7
α
9

39. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.
β
130
7
α
9
ArcSin, ArcCos & ArcTan
are all built into our
calculators

40. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.
7
β sin α =
130 130
7
α
9
ArcSin, ArcCos & ArcTan
are all built into our
calculators

41. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.
7
β sin α =
130 130
7
α −1 7
α = sin
130
9
this is calculator notation;
it means ‘ArcSin’
ArcSin, ArcCos & ArcTan
are all built into our
calculators

42. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.
7
β sin α =
130 130
7
α −1 7
α = sin
130
9
this is calculator notation;
it means ‘ArcSin’
ArcSin, ArcCos & ArcTan
are all built into our α ≈ 37.9°
calculators

43. Review from Advanced Algebra & Trigonometry
ArcSin (aka Inverse Sine)
If we know the ratios of the sides of a right triangle,
then we can find the angles using ArcSin, etc.
7
β sin α =
130 130
7
α −1 7
α = sin
130
9
this is calculator notation;
it means ‘ArcSin’
ArcSin, ArcCos & ArcTan
are all built into our α ≈ 37.9°
calculators
β = 90 − α ≈ 52.1°

44. An 18 foot ladder leans against a building. If the base
of the ladder is 5 feet from the base of the building,
what angle is formed by the ladder and the ground?

45. An 18 foot ladder leans against a building. If the base
of the ladder is 5 feet from the base of the building,
what angle is formed by the ladder and the ground?
18
θ
5

46. An 18 foot ladder leans against a building. If the base
of the ladder is 5 feet from the base of the building,
what angle is formed by the ladder and the ground?
5
18 cosθ =
18
θ
5

47. An 18 foot ladder leans against a building. If the base
of the ladder is 5 feet from the base of the building,
what angle is formed by the ladder and the ground?
5
18 cosθ =
18
−1 5
θ = cos
θ 18
5

48. An 18 foot ladder leans against a building. If the base
of the ladder is 5 feet from the base of the building,
what angle is formed by the ladder and the ground?
5
18 cosθ =
18
−1 5
θ = cos
θ 18
5 θ ≈ 73.9°

49. HW #3
Draw diagrams for your problems!!!
Pain is temporary. It may last a minute, or an hour, or a
day, or a year, but eventually it will subside and
something else will take its place. If I quit, however, it
lasts forever.
Lance Armstrong