Using cosine theorem to find triangle area

Using cosine theorem to find triangle area

S=1/2abSinc

Given the trilateral and cosine theorem, can we find the area of a triangle? Can't use Helen Qin Jiushao formula

It is known that the cosine theorem can be used to calculate the cos value of the angle, and then SiNx = √ 1-cos? X (Note: because the angle can not exceed 180 degrees in the triangle, so sin value is positive) triangle has an area formula s △ ABC = 1 / 2Ab · sinc = 1 / 2Ac · SINB = 1 / 2BC · Sina, and then the area can be calculated

Cosine triangle theorem In the acute angle △ ABC, if ∠ B = 2 ∠ C, then the range of B / C is

According to the sine theorem:
c/b=sinC/sinB
=sin2B/sinB
=2sinBcosB/sinB
=2cosB
∵ △ ABC acute triangle
∴0＜∠B＜π/2
0＜cosB＜1
0＜2cosB＜2
c/b=2cosB
∴0＜c/b＜2

In △ ABC, ∠ B = 120 °, AC = 7, ab = 5, then the area of △ ABC is______ .

According to cosine theorem, CoSb = 25 + BC2 − 49
2•BC•5=-1
2，
Get BC = - 8 or 3 (round off)
The area of △ ABC is 1
2•AB•BC•sinB=1
2×5×3×
Three
2=15
Three
Four
So the answer is: 15
Three
Four

Triangle cosine theorem In the triangle ABC, a = 2. B = radical 2, a = 45 ° to find the edge C

Cosine theorem
a²=b²+c²-2bc*cosA
4 = 2 + C? - 2 * root 2 * c * root 2 / 2
4=2+c²-2c
c²-2c-2=0
Just solve the equation

Draw an acute triangle and an obtuse triangle and make the three heights of the triangle

Draw the triangle and the three heights as follows:

How to draw the three heights of an obtuse triangle

Draw with a ruler --
The longest side can be drawn simply
The two short edges are extended with dashed lines before drawing,
That's it~``

Obtuse triangle acute triangle right triangle circumcircle center

The center of the circumscribed circle of an obtuse triangle is outside the triangle
The center of the circumcircle of an acute triangle is inside the triangle
The center of the circumscribed circle of a right triangle is on the hypotenuse of the triangle and is the midpoint of the hypotenuse

How many heights do acute, obtuse and right angled triangles have

There are three right angles and three obtuse triangles

Draw the three heights of acute angle, obtuse angle and right triangle

As shown in the figure, the blue line is the height! The two right sides of a right triangle are its other two heights! The dotted line of the obtuse triangle is the auxiliary line of height, which cannot be ignored!