Isosceles triangle
| [1-10] /245 | Disp-Num |
[1] 2022/10/03 21:03 50 years old level / High-school/ University/ Grad student / Useful /
Purpose of useTo compute the angle below the horizon of a straight line between two distant locations on the earth[2] 2022/06/12 09:13 30 years old level / An office worker / A public employee / Very /
Purpose of useNeeded top angle of triangle so that I could tell quickly if the crocheted triangle I was making was expanding at the correct rate to reach the base length at the right height[3] 2022/05/18 22:28 60 years old level or over / A retired person / Useful /
Purpose of useI wish to create a set of isosceles triangular templates for setting the fences of a table saw jig, for cutting pieces to make up polygonal wooden rings (e.g. a 12-sided ring). The rings are then glued together in a stack to form the rough shape of a segmented bowl that will be turned on a wood lathe.[4] 2022/04/13 22:10 60 years old level or over / Others / Very /
[5] 2022/04/07 02:55 20 years old level / An engineer / Very /
Purpose of useDESIGNING A DRILL BIT ANGLEComment/RequestMAKE BASE AND VERTEX ANGLE INPUT OPTION[6] 2022/04/04 09:47 60 years old level or over / A retired person / Very /
Purpose of useFiguring out how to build a regular gambrel roof on a shed so all rafters are the same size. Worked well.Comment/RequestThanks!![7] 2022/02/18 04:21 20 years old level / An engineer / Useful /
Purpose of use90 degree spray nozzle area covered[8] 2021/12/01 01:45 50 years old level / Others / Useful /
Purpose of usexmas tree design[9] 2021/11/10 09:18 50 years old level / An office worker / A public employee / Useful /
Purpose of useUsed formula to create a triangle template to use for a quilt project[10] 2021/10/20 00:34 50 years old level / Self-employed people / Useful /
Purpose of useDesigning Christmas tree frame for yard light displayThank you for your questionnaire.
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Use the Pythagorean Theorem for Right Triangles...
Question:
If I'm given a right triangle and two of its sides, how can I find the length of the third side? Can I do this if it's not a right triangle?
Answer
Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is \(a^2+b^2=c^2\), which is known as the Pythagorean Theorem. The theorem states that the hypotenuse of a right triangle can be easily calculated from the lengths of the sides. The hypotenuse is the longest side of a right triangle.
If you're given the lengths of the two sides it is easy to find the hypotenuse. Just square the sides, add them, and then take the square root. Here's an example:
Since we are given that the two legs of the triangle are 3 and 4, plug those into the Pythagorean equation and solve for the hypotenuse:
$$ a^2+b^2=c^2 $$ $$ 3^2+4^2=c^2 $$ $$ 25 = c^2 $$ $$ c = \sqrt{25} $$ $$ c = 5 $$
If you are given the hypotenuse and one of the legs, it's going to be slightly more complicated, but only because you have to do some algebra first. Suppose you know that one leg is 5 and the hypotenuse (longest side) is 13. Plug those into the appropriate places in the Pythagorean equation:
$$ a^2+b^2=c^2 $$ $$ 5^2+b^2=13^2 $$ $$ 25+b^2=169 $$ $$ b^2=144 $$ $$ b = 12 $$
As you can see, it is pretty simple to use the Pythagorean Theorem to find the missing side length of a right triangle. But -- what if it's not a right triangle? If you change that angle in the triangle there can obviously be any number of possibilities for the hypotenuse! Thus, you need more information to solve the problem. You can try using the Law of Sines or the Law of Cosines to determine side lengths in other triangles.