# 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 - 2bc*cos A.
6. b^2 = a^2 + c^2 - 2ac*cos B.

7. c^2 = a^2 + b^2 - 2bc

*cos 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)/2b

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)/2

*c =*

= (625 + 529 - 212)/[2(23)*14.56] = 0.173 --> A = 80 degree

= (625 + 529 - 212)/[2