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Math Help - Triangle Problem

  1. #1
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    Triangle Problem

    The triangle ABC is a right triangle with legs BC=3 and AC=4. The two angle trisectors of angle C intersect the hypotenuse. The longer of these trisectors has length (a(√(3))+b)/c), where gcf(a,b,c)=1

    Evaluate 15a-6b+32c.


    Even some preliminary explanation would help great deals. I need to figure it out tonight.
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  2. #2
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    Quote Originally Posted by LordHz View Post
    The triangle ABC is a right triangle with legs BC=3 and AC=4. The two angle trisectors of angle C intersect the hypotenuse. The longer of these trisectors has length (a(√(3))+b)/c), where gcf(a,b,c)=1

    Evaluate 15a-6b+32c.


    Even some preliminary explanation would help great deals. I need to figure it out tonight.
    Here's an easy but tedious method:

    C (0,0) A (4,0) B (0,3) Call the required length CP

    equation of line throug C and P is ..... equation of line through A and B is .....

    Solve simultaneously to find P then use Pythagoras to find length CP.

    Or use some clever geometry.....
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