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Math Help - I'm struggling with this question...Need Help!!!

  1. #1
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    Unhappy I'm struggling with this question...Need Help!!!

    A parcel of land is in the shape of an isosceles triangle. The base has length 425 feet; the other sides, which are of equal length, meet at an angle of 39 degree. How long are the two equal side?
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    Do you recall:

    1) The base angles of an isosceles triangle are congruent?
    2) The altitude perpendicular to the base bisects the apex angle and the base?
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  3. #3
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    Quote Originally Posted by nafita View Post
    A parcel of land is in the shape of an isosceles triangle. The base has length 425 feet; the other sides, which are of equal length, meet at an angle of 39 degree. How long are the two equal side?
    There are many approaches. Here are two:

    Let the unknown sides be of length x.

    Option 1. Drop a perpendicular from the vertex to the base and use the resulting right-triangle to solve for x:

    \sin (19.5^o) = \frac{212.5}{x} \, ......

    Option 2. Use the cosine rule to solve for x:

    425^2 = x^2 + x^2 - 2(x)(x) \cos (39^o) \, ........
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