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| Math Central | Quandaries & Queries |
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Subject: Height of a right triangle? The base of the right triangle is 50 ft. At the angle (on the base of the triangle) across from the right angle is labeled portion (a triangle within a triangle), the base of this little triangle is 10 ft. and the height is 6 ft. What equation can i use to solve this? The equation is what I need the most. Is it 6/10=50/x? Please help me. Thank you. |
Yes, Engelbert. It sounds like you are describing "similar" triangles. That's where all the angles of one triangle are the same as the angles of a second triangle. Here is the picture that we came up with based on your question:
In similar triangles the corresponding ratios of the side lengths are also the same, so the equation you came up with is not quite correct. If you say 6/10=50/x, then you are comparing the height-to-base ratio of the smaller triangle with the base-to-height ratio of the larger triangle. To get a correct equation (there is more than one) you have to compare the same ratios. So if you use base over height on one side of the equation you need to use base over height again on the other side. So one correct equation would be
6/10 = x/50.
Stephen and Haley.
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