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Homework Help: Right angle triangle trigonometry

  1. Dec 27, 2004 #1
    The question says determine theta

    I have a triangle with a hypotenuse of 3 cm
    opposite the angle theta is 2cm length
    and adjacent to that is unknown.

    I dont know how to solve this question I dont remember what theta is lol or how to punch it in the calculator what do I do plz help me refresh my mind. :confused:
     
  2. jcsd
  3. Dec 27, 2004 #2

    kreil

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    Gold Member

    You know that [tex]sin(\theta)=\frac{opp}{hyp}[/tex]

    therefore

    [tex]sin(\theta)=\frac{2}{3}[/tex]

    [tex]sin^{-1}(\frac{2}{3})=\theta[/tex]

    [tex]\theta=41.8 degrees[/tex]
     
  4. Dec 28, 2004 #3
    ok so whenever im solving for theta I use [tex]sin^-1[/tex] or do I use it whenever i am solving for any angle? what does [tex]sin^-1[/tex] do?

    also how did u know to use [tex]sin[/tex] ?
     
    Last edited: Dec 28, 2004
  5. Dec 28, 2004 #4
    SOH CAH TOA. Depends on what #s you have
     
  6. Dec 28, 2004 #5

    dextercioby

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    Science Advisor
    Homework Helper

    1.Yes,the equation:
    [tex] \sin \theta=a [/tex] is solved by applying on both sides of the equation the inverse function of "sin theta" (called [itex] \arcsin \theta [/itex]) which would giveu the result.Note the degree of generality:no (right) tringles involved,justmathematical functions.
    2.For any angle,for any argument of the function "sin",nit necessarily an angle.E.g.solve this equation for "x"
    [tex] \sin(x^{2}-4x+3)=-0.12 [/tex]
    "x"doesn't have the geomtrical interpretation of an angle,it's just "x",an arbitrary varible of a function f(x).
    3.Solve for the angle??? :rolleyes:
    4.In a right triangle,the sine of an angle is defined as the ratio between the opposide side and the hypothenuse.Since u were given both the opposite side ("opposite the angle theta is 2cm length") and the hypothenuse ("hypotenuse of 3 cm"),it was natural to use "sin".

    Daniel.
     
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