How Do You Find the Height of a Scalene Triangle?
To find the height of a scalene triangle, the formula for the area of a triangle is necessary. The equation is area = 1/2hb, where h is the height and b is the base. However, before using this formula, other calculations are required.
A scalene triangle has three sides that are unequal in length, and the three angles are also unequal. To find the height of a scalene triangle, the three sides must be given, so that the area can also be found. If a scalene triangle has three side lengths given as A, B and C, the area is given using Heron’s formula, which is area = square root{S (S – A)x(S – B) x (S – C)}, where S represents half the sum of the three sides or 1/2(A+ B+ C).
To find the height h from the given triangle area formula, rearrange it as h = 2(area)/b. Let b equal the side length B and find the area A with Heron’s formula. In triangles, the measurement for height is given at 90 degrees to the base.
