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Math Help - Isosceles' triangle circumcircle radius

  1. #1
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    Isosceles' triangle circumcircle radius

    Isosceles's triangle base is 16 cm and height is 4 cm. How much is isosceles' triangle circumcircle radius.
    Don't know where to start.
    There's a formula a/sin alpha=b/sin beta=c/sin gamma=2R where R is the radius of the circumcircle and a,b,c are sides. But I can't use it because I don't know the angles.
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  2. #2
    Junior Member
    Joined
    Aug 2005
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    to beggin with

    Hi,

    This should help you get started :

    First, you know (or should know) that the main height AH in the isosceles triangle ABC cuts the segment BC in half (because the triangle is isosceles and the Ah is the main height). So HC=BH=8. You can see that AH=1/2 HB.

    Now, finding angles :

    trigonometry : Because the triangle BHA is right-angled we can use the main sin, cos, tan (if not, we would have used the sin law* or the cos law).

    So tan(B) = AH/HB = 1/2 so B=tan^-1 (1/2) = 26.57 degrees so C=26.57 degrees and A=180-2*26.57=126.87 degrees

    Have fun !!

    * the sin law s the part of what you stated in your problem which is sin(A)/a=sin(B)/b=sin(C)/c where a is the side facing the angle A and b the side facing angle B... This law and the cosin law work in every triangle.
    Attached Thumbnails Attached Thumbnails Isosceles' triangle circumcircle radius-triangle.gif  
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