Q:

How do you find the altitude of a triangle?

A:

Quick Answer

The length of the altitude of a right triangle is equal to the geometric mean of the line segments of the hypotenuse. The geometric mean can be thought of as the average length of the two line segments.

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Full Answer

The altitude of a triangle is the line segment from any vertex of a triangle that is perpendicular to the side opposite of the vertex. The altitude of any triangle is easy to draw, but finding the length of the altitude can be difficult for triangles that aren't right triangles. Use the following steps to determine the length of the altitude for non-right triangles. If the area of the triangle is not a given value, then the length of the altitude must be determined using trigonometry.

  1. Determine the length of the base of the triangle
  2. The base of the triangle, in this case, will be the side of the triangle that is perpendicular to the altitude.

  3. Determine the area of the triangle
  4. If the problem is asking for the length of the altitude, usually the area will be a given value.

  5. Calculate the altitude
  6. Once the base and the area of the triangle have been determined, the length of the altitude of the triangle is equal to two times the quotient of the area divided by the base.

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