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Math Help - right triangle trig cont. w/ questions

  1. #1
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    right triangle trig cont. w/ questions

    ok so there.s a right triangle
    90 degrees on the bottom left, unknown on the bottom right
    and the top angle is 58 degrees
    the bottom side is 4.0 in length and the other sides are unknown
    solve for all sides and angles
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  2. #2
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    You can use the facts \sin \theta = \dfrac{Opposite}{Hypotenuse}\; \cos \theta = \dfrac{Adjacent}{Hypotenuse}\; \tan \theta = \dfrac{Opposite}{Adjacent}

    To get you started \sin 58^{\circ} = \dfrac{4}{c} assuming c is the hypotenuse. Now solve for c. You could now solve for the remaining side with either the pythagorean theorem or the cosine relation.

    For the angle, use the fact that all angles add to 180^{\circ}

    EDIT: Fixed some typos.
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  3. #3
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    Well, you know that a triangle has 180 degrees, and we've accounted for 90 + 58 = 148 of them. Thus, the remaining angle is 42 degrees.

    I'll call your "bottom" side x, your "vertical" side y, and your hypotenuse h (if I'm reading your description right!.

    So,  sin(58) = \frac{x}{h}

    But we know x = 4, so

     sin(58) = \frac{4}{h} .

    Can you find y?

    Edit: All angles are in degrees.
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  4. #4
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    so sin(58) =4/h and then this means that h=4.72 approximately
    according to the following: h=4.0(1/sin(58)=4.72=b correct?
    but i tried tangent for locating the adjacent side and my answer was 6.40 which is incorrect
    what happened?
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  5. #5
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     tan(58) = \frac{4}{y} \implies y = \frac{4}{tan(58)} =~ 2.5
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