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Math Help - Isoseles triangle

  1. #1
    Member OnMyWayToBeAMathProffesor's Avatar
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    Exclamation Isoseles triangle

    What is the measure of each base angle of an isosceles triangle if its vertex angle measures 42 degrees and its 2 congruent sides measure 12 units?

    How would you solve this problem i am completely lost. Please explain and give the answer,

    Thanks A Lot!
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  2. #2
    Senior Member
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    What is the measure of each base angle of an isosceles triangle if its vertex angle measures 42 degrees and its 2 congruent sides measure 12 units?

    How would you solve this problem i am completely lost. Please explain and give the answer,

    Thanks A Lot!
    We have two sides and the angle inbetween.

    We can drop a perpendicular bisector in the triangle, splitting the vertex angle up into 21 degrees and 21 degrees. (And thus we have two right triangles).

    Using Law of Sines:

    (Sin90)/12 = (Sin21)/b

    Solve for b:

    b = 11.2303

    Thus, the total base is 22.4606

    Nevermind, I just realized you wanted to find just the base angles; this is easy from just subtracting each angle 180 - 21 - 90 = 69 degrees, and obviously each of the base angles will be congruent since it's an isosceles triangle.
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    Smile Thanxs a lot

    thanxs a lot, i get it now
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