You only need to know its altitude.Ĭonstructing an altitude from any base divides the equilateral triangle into two right triangles, each one of which has a hypotenuse equal to the original equilateral triangle's side, and a leg ½ that length. It will have three congruent altitudes, so no matter which direction you put that in a shipping box, it will fit. What about an equilateral triangle, with three congruent sides and three congruent angles, as with △ E Q U below? Not every triangle is as fussy as a scalene, obtuse triangle. What about the other two altitudes? If you insisted on using side G U ( ∠ D) for the altitude, you would need a box 9.37 c m tall, and if you rotated the triangle to use side D G ( ∠ U), your altitude there is 7.56 c m tall. You would naturally pick the altitude or height that allowed you to ship your triangle in the smallest rectangular carton, so you could stack a lot on a shelf.Īltitude for side U D ( ∠ G) is only 4.3 c m. Think of building and packing triangles again. How to Find the Altitude of a TriangleĮvery triangle has three altitudes. To get the altitude for ∠ D, you must extend the side G U far past the triangle and construct the altitude far to the right of the triangle. To get that altitude, you need to project a line from side D G out very far past the left of the triangle itself. The altitude from ∠ G drops down and is perpendicular to U D, but what about the altitude for ∠ U? We can construct three different altitudes, one from each vertex.įor △ G U D, no two sides are equal and one angle is greater than 90 °, so you know you have a scalene, obtuse (oblique) triangle. The height or altitude of a triangle depends on which base you use for a measurement. How big a rectangular box would you need? Your triangle has length, but what is its height? Imagine you ran a business making and sending out triangles, and each had to be put in a rectangular cardboard shipping carton. Obtuse triangles - One interior angle is obtuse, or greater than 90 °Īn altitude is a line drawn from a triangle's vertex down to the opposite base, so that the constructed line is perpendicular to the base.Acute triangles - All interior angles are acute, or each less than 90 °.Oblique triangles break down into two types: ![]() ![]()
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