Find all formulas of high school sine and cosine theorem (must be all)

Find all formulas of high school sine and cosine theorem (must be all)

The sine cosine theorem is only two theorems
Positive: A / Sina = B / SINB = C / sinc
Remainder: a = B + C - 2abcos angle
b. C is the same in three forms

Know how to find the angle of three sides of a triangle according to sine theorem or cosine theorem If cosa = 0.258819045 is known How to find angle a

Three methods: 1
2. On the calculator, press Shift + cos + 0.258819045
3. Check the scientific type on the calculator provided by the computer system - tick in front of inv - input data - press cos

In △ ABC, if Sina: SINB: sinc = 2:3:4, then COSC is equal to () A. 2 Three B. −2 Three C. −1 Three D. −1 Four

According to the sine theorem, Sina: SINB: sinc = A: B: C = 2:3:4
Let a = 2K, B = 3k, C = 4K (k > 0)
According to the cosine theorem, COSC = A2 + B2 − C2
2ab=4k2+9k2−16k2
2•2k•3k＝−1
Four
Therefore, D

Cosine and sine theorems of triangles?

"Company" is a clerical error, "formula"?
Cosine theorem
a^2=b^2+c^2-2bc*cosA
b^2=c^2+a^2-2ac*cosB
c^2=a^2+b^2-2ab*cosC
a. B and C are the sides opposite angles a, B and C respectively
Sine theorem
a/sinA=b/sinB=c/sinC=2R
R is the radius of the circumscribed circle of the triangle

When a + B + C = 12, how to judge whether a triangle is an obtuse triangle?

If it's an obtuse angle c, C is the longest side
If a ^ 2 + B ^ 2C, CC > 12 (√ 2-1) is satisfied, an obtuse triangle can be formed

Given that a, B, C are three positive integers, and a + B + C = 12, can a triangle with edges a, B, C be an obtuse angle triangle? Why?

may not.
Let a ≤ B ≤ C, then an obtuse triangle must have
a+b＞c …… (1)
a²+b²＜c² …… II.
As a + B + C = 12, substituting it into Formula 1, we can get
A + b > 12-a-b, a + b > 6, a + B ≥ 7
∴ a²+b²＜c²=(12-a-b)²≤5²=25
However, a? + B? ≥ (a + b) 2 / 2 ≥ 7? / 2 = 49 / 2
∴ 49/2≤ a²+b² ＜25
There is no integer solution, so it will not form an obtuse triangle

In the obtuse angle triangle △ ABC, ∠ A is the obtuse angle ∠ B = 60 ° to find the range of ∠ C

Because ∠ a + ∠ B + ∠ C = 180 ° and ∠ B = 60 °
So ∠ a ＋∠ C = 120 °
Because ∠ A is an obtuse angle
So ∠ a > 90 ° so ∠ C

Know the length of the three sides of an obtuse triangle, how to find the height five hundred and fifty-five billion five hundred and fifty-five million five hundred and fifty-five thousand five hundred and fifty-five

Let one of the perpendicular lines passing through the apex of the obtuse angle be x, and the equation is formulated by Pythagorean theorem
Right and left sides are high squares, better solution, one variable linear equation

Do the three heights of an obtuse triangle intersect at one point

Why not,
The intersection of the three heights of a triangle is called the perpendicular center
When the triangle is an acute triangle, it is inside the triangle
When the triangle is a right triangle, at the right vertex
When the triangle is an obtuse angle triangle, it is outside the triangle

An obtuse triangle has three heights

Correct. One on the inside and two on the outside (extension)