Enter the length of the hypotenuse and the two segments it is divided into by the altitude to determine the length of the altitude in a right triangle using the Altitude Theorem.

Altitude Theorem Formula

The following formula is used to calculate the altitude in a right triangle:

h = √(a * b)

Variables:

  • h is the altitude of the right triangle
  • a is the length of segment 1 of the hypotenuse
  • b is the length of segment 2 of the hypotenuse

To calculate the altitude (h), take the square root of the product of the lengths of the two segments (a and b) that the hypotenuse (c) is divided into by the altitude.

What is the Altitude Theorem?

The Altitude Theorem is a principle in geometry that relates the lengths of the segments into which the altitude divides the hypotenuse of a right triangle to the length of the altitude itself. According to the theorem, the altitude from the right angle of a right triangle to its hypotenuse creates two right triangles that are similar to the original right triangle and to each other. The product of the lengths of the two segments of the hypotenuse is equal to the square of the length of the altitude.

How to Calculate Altitude using the Altitude Theorem?

The following steps outline how to calculate the altitude in a right triangle using the Altitude Theorem.

  1. First, determine the length of segment 1 of the hypotenuse (a).
  2. Next, determine the length of segment 2 of the hypotenuse (b).
  3. Use the formula h = √(a * b) to calculate the altitude (h).
  4. Finally, calculate the altitude (h) and check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Length of segment 1 of the hypotenuse (a) = 9 units

Length of segment 2 of the hypotenuse (b) = 16 units

Using the formula, the altitude (h) is calculated as:

h = √(9 * 16) = √144 = 12 units