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# How do you find the altitude of a triangle?

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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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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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## Related Questions

• A:

A right triangle, also known as a right-angled triangle, always has one angle at 90 degrees. The side directly opposite this angle is known as the hypotenuse, which is the longest side of a triangle.

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Pythagoras is most famous for the Pythagorean Theorem, which shows the relationship between the length of the two legs of a right triangle and the length of its hypotenuse. He is also famous for other aspects of his mathematical and philosophical insights. He was a mystic as well as a mathematician and founded a whole school of philosophy.

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• A:

The Pythagorean Theorem is used to find the length of the hypotenuse of a right triangle, a calculation which affords many practical uses, such as within the fields of construction, land surveying and navigation. The relationship between the two legs of a right triangle and the hypotenuse, shown by the equation a2 + b2 = c2, is known as the Pythagorean triplet, and its use in ancient megalithic construction is believed to predate the discovery of writing. The ancient Egyptians used a rope marked in the Pythagorean triples of 3, 4 and 5 to create right triangles and some evidence points to a possible use by Babylonian mathematicians.