Method 30 for solving right triangles

The inverse theorem of the Pythagorean theorem, which proves that the square of the sum of the two sides is equal to the square of the third side, which is a right triangle, the positive theorem, and the residual theorem.

Evidence congruence: HL's theorem Prove that an angle is a right triangle: prove that an angle is ninety degrees.

Corner Corner Corner Corner Edge Corner Edge Edge Edge RT

It is solved by constructing a right triangle.

Other Hand Sensitivity Methods:

1. The solution of the sinusoidal theorem, that is, a sina = b sinb =c sinc = 2r=d

2. Using the cosine theorem, it can be used directly to solve a class of problems of finding the third side of the two sides and angles of a known triangle or finding the triangle of the three sides of the known triangle; i.e. cos a = (b + c -a ) 2bc

The first type: know that an acute angle in a right triangle is opposite to the opposite side of this acute angle, and solve this type of right triangle.

Method: Firstly, another right angle can be obtained according to the mutual surplus of two acute angles of a right triangle, then the hypotenuse is obtained from the sinusoidal of the known acute angle, and finally the other right angle edge is obtained from the tangent of the known acute angle. Category II:

It is known that the acute angle of the right-angled triangle and the adjacent edge of the acute angle are resistant to bending, and the right-angled triangle is solved.

Method: Firstly, another right angle can be obtained according to the mutual remainance of two acute angles of a right triangle, then the hypotenuse can be obtained from the cosine of the known acute angle, and finally the other right angle edge can be obtained from the tangent of the known acute angle.

Method: Firstly, another right angle can be obtained according to the mutual interdependence of two acute angles of a right triangle, then the adjacent edge can be obtained from the chorus of Yu Chang of known acute angles, and finally the other right angle side can be obtained from the sine of known acute angles The fourth type: two right angles of a known right triangle is solved.

Method: First, the hypotenuse c was obtained from the Pythagorean theorem; These two acute angles are then found according to the tangent of the acute angles. Type 5: Knowing the right triangle with the right angle and the hypotenuse, solve the right triangle.

Method: First, another right-angled edge is found by the Pythagorean theorem, and then the sine of an acute angle is equal to the ratio of the right-angled edge to the hypotenuse, so as to find this acute angle, and finally the other acute angle is obtained by using the mutual remainance of two acute angles.

In a right triangle, there are five elements except the right angle, that is, three sides and two acute angles, and the process of finding all the unknown elements from the known elements in the right triangle except the right angle is called solving the right triangle.

In the process of solving right triangles, it is first necessary to clarify the definition of acute triangles:

The uppercase letter indicates the angle, the lowercase letter indicates the side length of the triangle, and the c represents the right-angle side length.

It can be seen that each formula contains 3 elements of a triangle, and when 2 of the 3 are known, it is converted into a unary equation, and the unknown elements can be found by solving the equation.

Depending on the known element species, the solutions of right triangles can be summarized into the following 4 categories, as shown in the table:

1. The Pythagorean theorem.

2. Solve the triangle formula a sina=b sinb=c sinc

In this way, it is basically o to find the edge and the angle.

The two right-angled edges are A and B respectively, and the hypotenuse is C.

a^2+b^2=c^2

Do you want to calculate the length of each side, or the degree of each corner?

Nope! This must be seen in the Sinine Cosine tangent cotangent table. There is a dedicated table!

Used to check. The junior high school teacher said that it was going to be sent in high school, but the high school teacher said that it was going to be sent in junior high school, and I still haven't seen what that watch looks like.

West building height = 30 * tan 45 ° = 30m

The west building is higher than the east building = 30 * tan 10 ° =

East Building Height=

Solution:1

Let the parabolic equation be y=a(x+1) 2-2

x=-2 y=1 substitution.

a(-2+1)^2-2=1

When the parabolic formula of a=3 is y=3(x+1) 2-2=3x 2+6x+1(1)0x=2, there is ymin=-3

When x=3, there is ymax=0

The process is detailed in the figure below.

Note that the denominator is rationalized.