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Triangle angles?

  1. Dec 17, 2011 #1
    I am stuck on the job; I need to find the angles.
    It’s not an angle or side based triangle, just a right triangle. The lengths are known, A-B-C. What I need to know is the angles, a-b-c. So, a=90*, what formula could I use to find b, and c? Sorry, please make it easy enough for me to work it out, I never made it past algebra and failed geometry.
  2. jcsd
  3. Dec 17, 2011 #2
    Well, you could use law of sines. Plug in your values and solve for the desired angles

    [tex]\frac{sin(a)}{A} = \frac{sin(b)}{B} = \frac{sin(c)}{C} = 2R[/tex]

    However, this is past algebra and sometimes covered at the end of geometry.
    Last edited: Dec 17, 2011
  4. Dec 17, 2011 #3
    If this is a right angled triangle, could you not use trigonometry.

    Cos(c) = adjacent/hypotenuse = B/A
    Sin(c) = opposite/hypotenuse = C/A
    Tan(c) = opposite/adjacent = C/B

    Similarly for angle b

    Cos(b) = C/A
    Sin(b) = B/A
    Tan(b) = B/C
  5. Dec 17, 2011 #4
    That's over my head. Can you please break it down?
  6. Dec 17, 2011 #5
    Right, so you have a right angled triangle. The angle a = 90. The side opposite of angle a = A. The side opposite of angle b = B. The side opposite of angle c = C.

    Now the longest side of a right angled triangle is known as the hypotenuse, this always happens to be the side opposite to the right angle, so side A = hypotenuse.

    Now if we consider angle b, it is the angle between the side A (hypotenuse) and the side C. We call the side C the adjacent side. Then side B is the opposite (because it is the side opposite of angle b).

    If we consider angle c, then A = hypotenuse, B = adjacent, C = opposite.

    Now there are functions that relate the sides and angles of a triangle.

    Cos (angle) = adjacent/hypotenuse
    Sine (angle) = opposite/hypotenuse
    Tan (angle) = opposite/adjacent

    This is how you get the equations i wrote above. Now you can find the cos, sine, and tan function on a standard scientific calculator. So if you want to find the angle you do the inverse function of the ratio of the sides.

    So depending what side you know, you can use either of the 3 equation

    angle = inverse cos(adjacent/hypotenuse)
    angle = inverse sine(opposite/hypotenuse)
    angle = inverse tan(opposite/adjacent)
  7. Dec 17, 2011 #6
    By using the law of sines, we get

    [tex]\frac{sin(a)}{A} = \frac{sin(b)}{B}[/tex]

    Since you know [itex]a[/itex], [itex]A[/itex], and [itex]B[/itex], you can solve for [itex]b[/itex].

    [tex]\frac{B\cdot sin(a)}{A} = sin(b)[/tex]
    [tex]sin^{-1}(\frac{B\cdot sin(a)}{A}) = b[/tex]

    Likewise, you can also solve for [itex]c[/itex]. Make sure your calculator setting is either on degrees or radians, depending on your situation.
    Last edited: Dec 17, 2011
  8. Dec 18, 2011 #7
    Thank you very much for the helping hand. Trigonometry is awesome.

    I understand now how to get the ratio. And I found how to use C, S, or T to change angle to a ratio (put in the angle and hit the C, S, or T key on the XP-W scientific calculator, to get the ratio of the sides.), but it was said: “so if you want to find the angle you do the inverse function of the ratio of the sides.”

    If: HYP = 26.1725, ADJ = 26, and OPP = 3, a = 90* so,
    COS (b) = C/A = .9934, or
    SIN (b) = B/A = .1146, or
    TAN (b) = B/C = .1154 …

    How is the inverse function executed on my calculator?
    Last edited: Dec 18, 2011
  9. Dec 18, 2011 #8
    I'm not sure if it's different for each calculator, but the inverse function is denoted cos^(-1), sin^(-1), tan^(-1).

    On my calculator it appears in yellow writing just above the sin, cos, and tan buttons.

    So i have to press shift then sin to get inverse sin, shift cos to get inverse cos, shift tan to get inverse tan.
  10. Dec 18, 2011 #9
    Tan(b) = B/C = opp/adj
  11. Dec 18, 2011 #10
    If: HYP = 26.1725, ADJ = 26, and OPP = 3, a = 90* so,
    COS (b) = C/A = .9934, or
    SIN (b) = B/A = .1146, or
    TAN (b) = B/C = .1154 …
    How is the inverse function executed on my calculator?
    Answer: INV- button
    So, COS ratio – INV button – COS button = angle = 6.58*pitch
    Thank you very much

    Finding the error is the hard part, fixing it is easy but rewarding. So let me reverse that, thank you gamer, you have a good eye.
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