1, triangle area formula: S= base × height ÷2.

This formula is used to calculate the area of a triangle, where the base is an edge of the triangle and the height is a line segment vertically connected to the vertex of the triangle from that edge. Multiply the length and height of the base and then divide by 2 to get the area of the triangle.

2. Sine theorem: a/sinA=b/sinB=c/sinC.

This theorem is used to calculate the size of three internal angles of a triangle, where A, B and C are the lengths of three sides of the triangle and A, B and C are the three internal angles of the triangle. Divide A, B and C by the values of sinA, sinB and sinC, respectively, and the sine values of the three internal angles are equal.

3. Cosine Theorem: A? =b？ +c？ -2000 BC.

This theorem is used to calculate the size of three internal angles of a triangle, where A, B and C are the lengths of three sides of the triangle and A is an internal angle of the triangle. Subtract the square of A from the sum of the square of B and the square of C, and then subtract 2 times the cosine of B times C to get the cosine of A. ..

Application of triangle:

Architecture: In architecture, triangles are widely used in structural design to increase the stability and strength of the structure. For example, the use of triangular frames can improve the wind and earthquake resistance of buildings. In addition, the triangular structure can also reduce the amount of materials, thus reducing the cost.

2. Mechanical design: In mechanical design, triangles are often used in structural design to ensure the stability and reliability of mechanical equipment. For example, triangular support and fixing devices can enhance the stability and seismic capacity of mechanical equipment.

3. Traffic signs: The triangle in traffic signs is an important sign to remind drivers to pay attention to traffic safety. For example, a white triangle with a black background indicates that there is an intersection or road construction area ahead, reminding drivers to slow down or change lanes.

4. Aerospace: In the aerospace field, triangles are widely used in the design and manufacture of aircraft. For example, triangular wings can provide better aerodynamic performance and stronger structural strength. In addition, the triangular rocket tail can improve the stability and reliability of the rocket.

5. Mathematics education: In mathematics education, triangles are widely used in geometry teaching. For example, using triangles can help students understand the relationship among angles, side lengths and areas, and learn how to use trigonometric functions for calculation.