Trigonometry and triangles

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Trigonometry and triangles

Trigonometry and triangles

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  • There is a couple ways to do the first problem. Then can use Pythagorean theorem.

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  • 1. Trigonometry and Triangles
    Michael Schmidt
  • 2. Trigonometry
    Sine Cosine Tangent
    Length of triangle legs
    Angle of triangle corners
    Area of triangles
    What we are doing
  • 3. Branch in Mathematics
    Uses trig functions
    Triangles
    Mostly right triangles
    Uses relationships to find unknowns
    Trigonometry
  • 4. θ (Theta)
    Adjacent leg (A)
    Opposite leg (O)
    Hypotenuse (H)
    Key Terms
    H
    O
    θ
    A
  • 5. SOH: sin θ =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
    CAH: cos θ =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
    TOA: tan θ =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
     
    SOH CAH TOA
  • 6. sin 37° =
    cos37° =
    tan 37° =
    SOH CAH TOA continued
    21𝑓𝑡35𝑓𝑡
    28𝑓𝑡35𝑓𝑡
    21𝑓𝑡28𝑓𝑡
     
    35ft
    21ft
    37°
    28ft
  • 7. What is given?
    Which trig function?
    Finding the side length
    12ft
    sin 30° = 𝑋12𝑓𝑡
     
    X
    sin 30°1 = 𝑋12𝑓𝑡
     
    X= 6ft
    30°
  • 8. Using trig, find unknown
    tan 20° = 𝑋6𝑚
     
    1
     
    X
    X= 2.18m
    20°
    6m
    X
    cos 45° = 8𝑖𝑛𝑥
     
    1
     
    45°
    X= 11.31in
    8in
  • 9. What is known?
    tan θ = 34
    Use 𝑡𝑎𝑛−1
    𝑡𝑎𝑛−1( 34 ) = θ
    θ = 36.86°
     
    Using trig to find θ
    3’
    θ
    4’
  • 10. sin θ = 10𝑚15𝑚
    𝑠𝑖𝑛−1(10𝑚15𝑚 ) = θ
    θ = 41.81°
     
    Solve for θ
    θ
    15m
    10m
    cos θ = 7𝑐𝑚9𝑐𝑚
    𝑐𝑜𝑠−1(7𝑐𝑚9𝑐𝑚 ) = θ
    θ = 38.94°
     
    9cm
    θ
    7cm
  • 11. Area of triangle
    A = 𝐵𝐻2
    A = 15∗102 = 75𝑚2
     
    Finding the Area
    10m
    15m
  • 12. What is given?
    What is needed?
    How is it found?
    tan60 = 𝐵10
    A =17.32𝑐𝑚∗10𝑐𝑚2
     
    Finding area with trig
    60°
    10cm
    B =17.32cm
    =86.6𝑐𝑚2
     
  • 13. Given
    Needed
    sin50 = 𝐻11
    A= 13∗8.432
     
    Non right triangles
    H= 8.43in
    11in
    A=54.8𝑖𝑛2
     
    50°
    13in
  • 14. cos 60 = 𝐻22
    Pythagorean theorem for the base
    A= 19.05∗112
     
    Find area of triangle
    H=11in
    60°
     
    22in
    A=104.78𝑖𝑛2
     
  • 15. Given
    Needed
    B= X+Y
    tan 45 = 𝑥16
    tan 30 = 𝑦16
    B=25.24cm
     
    Find area of triangle continued
    Height = 16cm
    16cm
    45°
    30°
    X
    Y
    X=16cm
    Y=9.24cm
    A=16∗25.242
     
    =201.92𝑐𝑚2
     
  • 16. A 6ft tall man is standing in front of a light. The light is casting a shadow. If the angle of depression at the man’s head is 60° how long is the shadow?
    Story Problems
    tan 60 = 𝐿6
     
    L=10.39ft
    60°
    6ft
    L
  • 17. Story problems
    There is a window 33ft up a building and the only ladder is 40ft long. For safety reasons the ladder is leaned against the building at 52°. Will the ladder reach the window?
    sin 52 = 𝐻40
    H=31.52ft
     
    40ft
    No, the ladder will not reach the window.
    52°
  • 18. SOH CAH TOA is key
    Find the Given and Needed
    Make own right triangle
    Draw a picture
    Wrap up