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Math Help - What is the length from B to C? What is the area of triangle?

  1. #1
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    What is the length from B to C? What is the area of triangle?

    Diagram here: http://img172.imageshack.us/img172/1344/trig.jpg

    What is the length from B to C?

    What is the area of triangle?
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  2. #2
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    Use the Law of Cosines to find the length of BC:
    \begin{aligned}<br />
BC^2 &= AB^2 + AC^2 - 2(AB)(AC)\cos A \\<br />
BC^2 &= 30^2 + 12^2 - 2(30)(12)\cos 45^{\circ} \\<br />
BC^2 &\approx 534.88 \\<br />
BC &\approx 23.13<br />
\end{aligned}
    So the length of BC is about 23.13 m.

    Then use Heron's formula to find the area. If you have a triangle with side lengths a, b & c, the formula is
    A = \sqrt{s(s - a)(s - b)(s - c)}
    where
    s = \frac{a + b + c}{2}

    In our case:
    s \approx \frac{30 + 12 + 23.13}{2} \approx 32.56
    and
    A \approx \sqrt{32.56(32.56 - 30)(32.56 - 12)(32.56 - 23.13)} \approx \sqrt{16200} \approx 127.28

    So the area of the triangle is about 127.28 sq. m.


    01
    Last edited by yeongil; July 5th 2009 at 09:37 PM. Reason: Finished the problem
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  3. #3
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    wht is the area

    thanks. what is the area? i dont know which side is the base, i know its 1/2 x base x height
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  4. #4
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    Quote Originally Posted by olivia59 View Post
    thanks. what is the area? i dont know which side is the base, i know its 1/2 x base x height
    there are more ways to find the area of a triangle than 1/2*base*height. there is, for example, 1/2*B*C*sinA and the like
    in the answer given by yeongil, Heron's formula was used Heron's formula - Wikipedia, the free encyclopedia
    hope this helps
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