Finding the Base of an Isosceles Triangle | Formulas and Methods

base of an isosceles triangle

The base of an isosceles triangle is the side of the triangle that is different in length from the other two sides

The base of an isosceles triangle is the side of the triangle that is different in length from the other two sides. In an isosceles triangle, two of the sides are equal in length, creating two congruent angles opposite those sides. The third side, known as the base, is not equal in length to the other two sides and is opposite the base angle.

To find the base of an isosceles triangle, you need to know the length of at least one of the congruent sides and either the measure of one of the base angles or the height of the triangle. The height of the triangle is the perpendicular distance from the base to the opposite vertex.

If you know the length of one of the congruent sides and the height, you can use the formula for the area of a triangle: A = (1/2) × base × height. Solving for the base, you get base = (2 × area) / height.

If instead, you know the length of one of the congruent sides and the measure of one of the base angles, you can use the Law of Cosines. The formula is:

c^2 = a^2 + b^2 – 2ab × cos(C)

Where c is the length of the base (opposite the angle C), and a and b are the lengths of the congruent sides (adjacent to angle C). By rearranging the formula, you can solve for c:

c = √(a^2 + b^2 – 2ab × cos(C))

In summary, the base of an isosceles triangle is the side that is not congruent to the other two sides. Its length can be found using the formula for the area of a triangle and the height or by using the Law of Cosines if the length of one congruent side and the measure of one base angle are known.

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