How to Find the Altitude of a Triangle: Methods and Formulas

Altitude of a triangle

The altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side or to the line that contains the opposite side

The altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side or to the line that contains the opposite side. It is also known as the height of the triangle.

To find the altitude of a triangle, you can use various methods depending on the given information. Here are three common methods:

1. Using the formula: If you are given the length of the base and the area of the triangle, you can use the formula:

Altitude = (2 * Area) / Base

Let’s say the length of the base is “b” and the area of the triangle is “A”. Plugging these values into the formula will give you the altitude.

2. Using the length of the sides: If you are given the lengths of the three sides of the triangle, you can use Heron’s formula to find the area of the triangle. Once you have the area, you can follow the formula mentioned in the previous method to calculate the altitude.

3. Using trigonometry: If you know the length of one side and the measure of the angle formed by that side and the altitude, you can use trigonometric ratios to find the altitude. The most commonly used trigonometric ratio for finding the altitude is the sine ratio. The formula is:

Altitude = (Side * sin(angle)) / sin(90°)

Let’s say the length of the side is “a” and the measure of the angle is “θ”. By substituting these values into the formula, you can calculate the altitude.

It’s important to note that the altitude will vary depending on which vertex it is drawn from. Each of the three vertices can be used to find a different altitude, resulting in three possible altitudes for a triangle.

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