Question #a98e1
1 Answer
Solving a triangle ABC means finding the value of an angle, or a side, knowing some values of other sides and angles. There are a few Formulas to use, depending of the 2 types of triangles.
Right triangle. Besides the Pythagor Formula (c^2 = a^2 + b^2), there are 3 basic formulas:
1. sin^2 A + cos^2 A = 1.
2. 1 + tan^2 A = 1/cos^2 A.
3. 1 + cot ^2 A = 1/sin^2 A.
General triangle. There are 4 formulas, with a, b, and c the sides of the triangle ABC.
4. a/sin A = b/sin B = c/sin C.
5. a^2 = b^2 + c^2 - 2bccos A.
6. b^2 = a^2 + c^2 - 2accos B.
7. c^2 = a^2 + b^2 - 2bccos A..
Example. Given a = 25 cm; b = 23; c = 14.56; find angle A.
Solution. Use Formula 5 and calculator to compute cos A.
cos A = (b^2 + c^2 - a^2)/2bc =
= (625 + 529 - 212)/[2(23)*14.56] = 0.173 --> A = 80 degree
