How to Find One Side of an Isosceles Triangle
- 1). To find the unknown base of an isosceles triangle, using the following formula: 2 * sqrt(L^2 - A^2), where L is the length of the other two legs and A is the altitude of the triangle. For example, given an isosceles triangle with legs length 4 and altitude length 3, the base of the triangle is: 2 * sqrt(4^2 - 3^2) = 2 * sqrt(7) = 5.3.
- 2). To find the unknown leg length with a given base length and altitude, use the following formula: sqrt(A^2 - (B / 2)^2), where A is the altitude and B is the length of the base. For example, given an isosceles triangle with base length 6 and altitude 7, the leg lengths are: sqrt(7^2 + (6 / 2)^2) = sqrt(58) = 7.6.
- 3). To find the altitude of an isosceles triangle with a known leg length and base length, use the following formula: sqrt(L^2 - (B / 2)^2, where L is the leg length and B is the base length. For example, given a triangle with leg length 8 and base length 6.5, the altitude must be: sqrt(8^2 - (6.5 / 2)^2 = sqrt(53.4) = 7.3.
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