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Math Help - Solving triangle ABC using given measurements

  1. #1
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    Solving triangle ABC using given measurements

    I was not paying attention in class when this was taught and now I'm completely lost

    right triangle ABC
    B=40 degrees

    side a=14

    what do I do next?
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  2. #2
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    Well if it's a right triangle, one angle is 90. You said another is 40, and all three angles of a triangle should equal 180. Is side A the hypotenuse or one of the other sides?
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  3. #3
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    yeah so A=50 B=40 C=90
    a is not the hypotenuse, c is
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  4. #4
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    Here's the steps, but I don' know offhand how to do each of them:

    If you know two angles and any side:

    • Use the Sum of the Angles with the two angles to find the third angle
    • Use the Law of Sines and plug in the values for the two angles and the side
    • Solve for the side
    • Use the Law of Sines with an angle, the side opposite it, and the angle opposite the side you still don't know to find that side
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  5. #5
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    The Law of Sines defines the relationship between the sine of any angle in a triangle and the side opposite it. The formula is: a/sinA = b/sinB = c/sinC
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  6. #6
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    lengths - a = 14cm
    - b = 16.68cm
    -c = 21.78cm

    angles - A = 50
    - B = 40
    - C = 90
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  7. #7
    A riddle wrapped in an enigma
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    Quote Originally Posted by chelsealover25 View Post
    lengths - a = 14cm
    - b = 16.68cm
    -c = 21.78cm

    angles - A = 50
    - B = 40
    - C = 90
    Are you sure about the values for b and c?
    Attached Thumbnails Attached Thumbnails Solving triangle ABC using given measurements-right-triangle.jpg  
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  8. #8
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    Quote Originally Posted by emmahlav View Post
    I was not paying attention in class when this was taught and now I'm completely lost

    right triangle ABC
    B=40 degrees

    side a=14

    what do I do next?
    You can use simple trigonometric definitions. No need to get fancy.
    cos(40^o) = \frac{14}{c} \implies c = 18.2757

    and
    tan(40^o) = \frac{b}{14} \implies b = 11.7474

    And you can check your answers using the Pythagorean Theorem: 14^2 + b^2 = c^2.

    -Dan
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