To solve a scalene triangle we need three element: one of wich must be a side.
Now we explain all cases.
Case a) knowing one side and adjacent angles of a triangle:
To solve and determine all other paramether of the triangle we follow these steps:
- We know: , we looking for
- The sum of internal angle into a triangle is a180°, then .
- Using the Law of sines we obtain other two side:
- We know , we looking for
- Using Law of cosines we can determine c
- similary we can obtain other angles solving Law of cosines by cosine:
There is another way to solve the scalene triangle in this case:
- Frist of all determine
Now we have the parameters for solve triangle with:
Follow these steps:
- By Law of sines determine another angle:
The faster way in a calculator is use law o cosines in inverse notation:
There is another way with Briggs formulas:
- Determine semiperimeter:
- Use Briggs for determine tangents of half-angles:
And then solve inverse functions for the value of angles.