What is half of dfrac 6 12

Triangle 6 12 12

Acute-angled isosceles triangle.

Pages: a = 6 b = 12 c = 12

Surface: T = 34.85768501159
Scope: p = 30
Semiperimeter (half circumference): s = 15

angle & angle; A = α = 28.95550243719 ° = 28 ° 57'18 ″ = 0.50553605103 rad
angle & angle; B = β = 75.52224878141 ° = 75 ° 31'21 ″ = 1.31881160717 rad
angle & angle; C = γ = 75.52224878141 ° = 75 ° 31'21 "= 1.31881160717 rad

Height: Ha = 11.61989500386
Height: Hb = 5.80994750193
Height: Hc = 5.80994750193

Middle: ma = 11.61989500386
Middle: mb = 7.34884692283
Middle: mc = 7.34884692283

Inradius: r = 2.32437900077
Perimeter radius: R = 6.19767733539

Vertex coordinates: A [12; 0] B [0; 0] C [1.5; 5.80994750193]
Main emphasis: SC [4.5; 1.93664916731]
Coordinates of the circumcircle mean: U [6; 1.54991933385]
Coordinates of the inscribed circle: I [3; 2.32437900077]

Outside angles of the triangle:
& angle; A '= α' = 151.0454975628 ° = 151 ° 2'42 ″ = 0.50553605103 rad
& angle; B '= β' = 104.4787512186 ° = 104 ° 28'39 ″ = 1.31881160717 rad
& angle; C '= γ' = 104.4787512186 ° = 104 ° 28'39 ″ = 1.31881160717 rad

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1. The circumference of the triangle is the sum of the lengths of its three sides

2. Semiperimeter of the triangle

The radius of the triangle is half of its circumference. The semiperimeter often appears in formulas for triangles that are given their own name. Due to the triangle inequality, the longest side of a triangle is smaller than the semiperimeter.

3. The triangle area with Heron's formula

Heron's formula gives the area of ​​a triangle when the length of all three sides is known. It is not necessary to first calculate angles or other distances in the triangle. Heron's formula works equally well for all cases and types of triangles.

4. Calculate the height of the triangle from its contents.

There are many ways to find the height of the triangle. The easiest way is by area and basic length. The area of ​​a triangle is half the product of the length of the base and the height. Each side of the triangle can be a base; There are three bases and three heights. The triangle height is the perpendicular line segment from a vertex to a line that contains the base.

5. Calculation of the inner angles of the triangle with a cosine law

The law of cosine is useful for finding the angles of a triangle when we know all three sides. The cosine rule, also known as the cosine law, involves all three sides of a triangle with an angle of a triangle. The law of cosine is the extrapolation of Pythagorean theorem for each triangle. Pythagorean theorem only works in a right triangle. The Pythagorean theorem is a special case of the cosine theorem and can be derived from it because the cosine of 90 ° is 0. It's best to find the angle opposite the longest side first. With the cosine law there is also no problem (as with the sine law) with obtuse angles, since the cosine function is negative for obtuse angles, positive for right zero and for acute angles. We also use the inverse cosine, known as the arccosine, to determine the angle from the cosine value.

a2 = b2 + c2−2bccosαα = arccos (2bcb2 + c2 − a2) = arccos (2⋅12⋅12122 + 122−62) = 28∘57′18 "b2 = a2 + c2−2accosββ = arccos (2aca2 + c2 − b2) = arccos (2⋅6⋅1262 + 122−122) = 75∘31′21 "γ = 180∘ − α − β = 180∘ − 28∘57′18" −75∘31′21 "= 75∘31′21"

6. Inradius

A circle of a triangle is a circle that touches each side. An incircle center is called an incenter and has a radius named inradius. All triangles have a center point that is always inside the triangle. The center point is the intersection of the three bisectors. The product of the in-radius and the semiperimeter (half the circumference) of a triangle is its area.

7. Perimeter radius

The perimeter of a triangle is a circle that goes through all of the vertices of the triangle, and the perimeter of a triangle is the radius of the perimeter of the triangle. The center point (center of the circle) is the point at which the perpendicular bisectors of a triangle intersect.

R = 4rsabc = 4⋅2.324⋅156⋅12⋅12 = 6.2

8. Calculation of the median

A median of a triangle is a line segment that connects one vertex with the midpoint of the opposite side. Each triangle has three medians that all intersect at the center of gravity of the triangle. The centroid divides each median into parts at a 2: 1 ratio, with the centroid twice as close to the midpoint of one side as it is to the opposite vertex. We use Apollonius' theorem to calculate the length of a median from the lengths of its side.

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