How to Solve Sides of an Isosceles Triangle
The beauty of trigonometry is that you can make so much out of so little. For instance, to solve the sides "a" and "b" of an isosceles triangle, all you need to know is the length of the base "c" and the value of the angle C opposite it. By plugging the latter two values into a trigonometric equation, you can solve for everything else -- including the values of the remaining sides and angles (B and C).
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Instructions
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1
Plug the values you know (c and C) into the Law of Cosines, which reads: c^2 = a^2 + b^2 - 2ab(cosC). Thus, given a base (c) of 425 and the angle opposite it (C) of 39 degrees, the equation becomes the following:
425^2 = a^2 + b^2 - 2ab(cos(39))
180,625 = a^2 + b^2 - 2ab(0.778)
180,625 = a^2 + b^2 - 1.556(ab)
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2
Simplify the equation. Because the sides of an isosceles "a" and "b" are equal to one another, you can change "b" to "a." Thus, the equation becomes the following:
180,625 = a^2 + a^2 - 1.556a^2
180,625 = 0.444a^2
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3
Solve for "a." According to the equation outlined as an example, "a" equals the square root of 180,625/0.444, or √406,813, or 637.81.
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4
Equate "a" and "b." Thus, the sides "a" and "b" of the isosceles triangle are both equal to 637.81.
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