Who can help me sum up some knowledge about right triangle

Who can help me sum up some knowledge about right triangle

1、 Knowledge block diagram
According to the knowledge network structure diagram, students can say the contents of each number in the order of numbers
2、 Knowledge points
1. Pythagorean theorem (inverse theorem) and its application
The application of Pythagorean theorem mainly includes: (1) finding the third side from both sides of a right triangle; (2) proving the square relation of some line segments in a triangle; (3) making a line segment of length
Pythagorean theorem the main application of the inverse theorem is to determine whether a triangle is a right triangle
2. Acute trigonometric function
4. The range of trigonometric function of acute angle and its increase or decrease
A is the acute angle
0＜sinA＜1；0＜cosA＜1；tanA＞0,
The sine and tangent of acute angle a increase (or decrease) with the increase (or decrease) of angle, and the cosine of acute angle a decrease (or increase) with the increase (or decrease) of angle
If a and B are acute angles and a > b, then Sina > SINB, cosa < CoSb, Tana > tanb
5. Solve right triangle
(1) The relationship between edges and corners in a right triangle:
① Trilateral relation: A2 + B2 = C2;
② The relationship between two acute angles: ∠ a ＋ B = 90 °;
③ The relationship between edges and corners: Sina = CoSb =
(2) The method of solving right triangle can be summarized as follows: "use sine and cosine when there is an oblique (hypotenuse), use tangent when there is no oblique (tangent), rather multiply than divide, take the original and avoid the middle."
(3) The meanings of terms in practical problems are as follows
① Elevation angle and depression angle: when measuring, the angle between line of sight and horizontal line is called elevation angle when looking from bottom to top; the angle between line of sight and horizontal line is called depression angle when looking from top to bottom, as shown in Figure 1
② Slope angle and slope: the angle between slope and horizontal plane is called slope angle, and α in Figure 2 is slope angle; the ratio of vertical height h and horizontal distance L of slope is called slope
3、 Method of thinking
1. The idea of combination of number and shape: in front of learning the right triangle, we studied it more from the "shape", but now we use the acute angle trigonometric function to solve the right triangle, mainly from the "number". When solving specific problems, we should draw its plane or cross-section diagram, and calculate the number according to the relationship between the edges and corners in the diagram
2. The idea of equation: when solving a right triangle, we often solve the problem by setting an unknown sequence equation
3. The idea of transformation: when seeking trigonometric function value and right triangle, we often use the meaning of trigonometric function to realize the mutual transformation of edges and angles, and use the trigonometric function relationship of mutual complementary angle to realize the mutual transformation of "sine" and "cosine"