Base of an isosceles triangle Chapter 5 (p. 244)
The side of an isosceles triangle that is not one of the legs
The base of an isosceles triangle is one of the sides that is not congruent to the other two sides. In an isosceles triangle, the two congruent sides are opposite to each other, and they form the two equal angles at the vertex. The base is the side that separates the two equal angles.
In order to find the length of the base of an isosceles triangle, you will need to know either the lengths of the two congruent sides or the measure of one of the equal angles. Once you have this information, you can use trigonometry or other methods to find the length of the base.
For example, if you know the lengths of the two congruent sides, you can use the Pythagorean theorem to find the length of the base. If the two congruent sides have length a and the base has length b, then:
a² = (b/2)² + h²
Where h is the height of the triangle (the distance from the base to the vertex). Solving for b, we get:
b = 2√(a² – h²)
Alternatively, if you know the measure of one of the equal angles, you can use trigonometry to find the length of the base. Let’s say that the two congruent sides have length a and the measure of one of the equal angles is θ. Then:
b = 2a sin(θ/2)
Where sin is the sine function. This formula is derived from the fact that the height of the triangle can be found using the formula:
h = a cos(θ/2)
Where cos is the cosine function. Then, using the formula for the area of a triangle (A = 1/2 bh), we can find the length of the base:
b = 2A/h = 2a sin(θ/2)
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