How do you find length of scalene triangle?

Answer 1

Usually, you are given at least a length and an angle

Using these two known parts of a scalene triangle

Imply the sine laws

SinA/a = SinB/b = SinC/c

Where A is the angle, and a is the length

You need to know at least three parts, either two angles and a side, or two sides and an angle to find the unknown using the above pattern.

Use two out of the three equated sine equations above with your known values

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Original answerer replies:

It is not much help to give an answer that suggests using the sine law when it may not be of any help. The proper answer is that it will all depend on what you are given. And that is the bottom line.

You cannot assume that you are given "at least a length and an angle". You could be given two lengths and an altitude, for example. In that case the sine law would be useless. Or you could be given two sides and a median - again no help from the sine law. In any of these cases, some hard trigonometry is required before you can get to the answer.

Furthermore, if you are given two sides and the included angle, you have a, b and C or sin(C). So you cannot evaluate any of the three ratios to use the sine rule because you have only one of the two components in each ratio. Alternatively, if you have two sides and an angle other than the included angle, you have the "ambiguous case" where the triangle can have two possible shapes.

In short, I believe that the sine rule cannot help unless you have a lot more information about the triangle.