Verify that the triangle has two sides of equal length and is therefore isosceles. If you label the three corners of a triangle A, B and C, two of the sides, AB, AC and BC, must be of equal length.
If AB equals AC, the altitude is the perpendicular line from A to the midpoint, M, of the side BC. A, M and C form the corners of a new triangle, which is a right triangle because one of the angles is a right angle, 90 degrees.
Derive the formula for the altitude from the Pythagorean theorem, which applies to right triangles. It states that c^2 = a^2 + b^2, where c is the length of the hypotenuse, the side opposite the right angle and the longest side in a right triangle, and a and b are the lengths of the other two sides. Therefore, a is equal to the square root of c^2 - b^2, the equation for the altitude of an isosceles triangle.
AM is the altitude a, MC is b, and AC is the hypotenuse c. Note that MC is half of BC, which is the side of the isosceles triangle not equal to the other two sides. If the length of BC is 10 meters, the length of MC is 5 meters. If AC is 8 meters, the altitude is equal to the square root of 8^2 - 5^2, which is the square root of 39, or approximately 6.24.