A, Helen formula:
Helen formula has also been translated into Helen formula, Hailong formula, Hero formula and Helen-Qin formula. It is a formula for directly calculating the area of a triangle by using the side lengths of three sides of the triangle. The expression is: S=√p(p-a)(p-b)(p-c), which is characterized by beautiful form and easy memory.
This formula was first drawn by the ancient Greek mathematician Archimedes, because it first appeared in Helen's book Geodesy, so it was called Helen's formula. China and Qin also put forward a similar formula, which is the so-called triclinic quadrature.
Second, cosine theorem.
Cosine theorem, the basic theorem of Euclidean plane geometry. Cosine theorem is a mathematical theorem describing the relationship between the length of three sides in a triangle and the cosine value of an angle. It is a generalization of Pythagorean theorem in general triangles, and Pythagorean theorem is a special case of cosine theorem.
Cosine theorem is an important theorem to reveal the relationship between the angles of a triangle. It can be directly used to solve the third side of a triangle with known two sides and included angle or a triangle with known three sides. Cosine theorem will be more convenient and flexible to use if it is modified and properly transferred to other knowledge.
Precautions:
1. When using sine theorem to solve the diagonal of two sides and one side of a known triangle and the diagonal of the other side, and then solving other sides and angles, sometimes there may be one solution, two solutions or no solution, so we should pay attention to the classification discussion.
2. When judging the triangle shape, the common factor cannot be omitted on both sides of the equation, and the common factor should be extracted by shifting the term to avoid missing the solution.
3. When the area of a triangle is known, the sine theorem or cosine theorem is generally used to realize the mutual transformation of sides and angles to solve the problems related to the area.