How do you find the third altitude of a triangle with the two other altitudes? I have the altitudes 12 and 14.
Do you know the area, or some other information about the triangle?
With just two altitudes, an infinite number of triangles can be formed.
To find the third altitude of a triangle, we need to know more information about the triangle, such as the side lengths or angles. The altitudes of a triangle alone are not sufficient to determine the length of the third altitude without additional information.
Altitudes are perpendicular segments drawn from each vertex of the triangle to its opposite side. Knowing the lengths of two altitudes, in this case, 12 and 14, does not uniquely determine the length of the third altitude.
To find the missing information about the triangle, you will need either one or both of the following:
1. The side lengths of the triangle: Knowing the lengths of the sides can help us use the formula for the area of a triangle: Area = 1/2 * base * height. Since the base of each altitude is one of the sides of the triangle, by using the area formula, we can find the missing altitudes.
2. The angles of the triangle: Knowing the angles can allow us to use trigonometric functions, such as sine, cosine, or tangent, to find the sides or altitudes of the triangle.
Without either of these pieces of information, finding the length of the third altitude is not possible.