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.
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