If we denote the length of the altitude by h c, we then have the relation In a right triangle, the altitude with the hypotenuse c as base divides the hypotenuse into two lengths p and q. It is common to mark the altitude with the letter h (as in height), often subscripted with the name of the side the altitude comes from. Also the altitude having the incongruent side as its base will form the angle bisector of the vertex. In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that side as its foot. The altitudes are also related to the sides of the triangle through the trigonometric functions. Thus the longest altitude is perpendicular to the shortest side of the triangle. It is a special case of orthogonal projection.Īltitudes can be used to compute the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude of that vertex. The length of the altitude, often simply called the altitude, is the distance between the base and the vertex. The intersection between the extended base and the altitude is called the foot of the altitude. This line containing the opposite side is called the extended base of the altitude. forming a right angle with) a line containing the base (the opposite side of the triangle). In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. Three altitudes intersecting at the orthocenterĪn altitude is the perpendicular segment from a vertex to its opposite side.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |