### Right scalene triangle.You are watching: Angles in a 5 12 13 triangle

Sides: a = 5   b = 12   c = 13Area: T = 30Perimeter: p = 30Semiperimeter: s = 15Angle ∠ A = α = 22.6219864948° = 22°37"11″ = 0.39547911197 radAngle ∠ B = β = 67.3880135052° = 67°22"49″ = 1.17660052071 radAngle ∠ C = γ = 90° = 1.57107963268 radHeight: ha = 12Height: hb = 5Height: hc = 4.61553846154Median: ma = 12.25876506721Median: mb = 7.81102496759Median: mc = 6.5Inradius: r = 2Circumradius: R = 6.5Vertex coordinates: A<13; 0> B<0; 0> C<1.92330769231; 4.61553846154>Centroid: CG<4.97443589744; 1.53884615385>Coordinates the the circumscribed circle: U<6.5; -0>Coordinates the the inscribed circle: I<3; 2>Exterior (or external, outer) angle of the triangle: ∠ A" = α" = 157.3880135052° = 157°22"49″ = 0.39547911197 rad∠ B" = β" = 112.6219864948° = 112°37"11″ = 1.17660052071 rad∠ C" = γ" = 90° = 1.57107963268 radCalculate one more triangle Show an ext digits
How did us calculate this triangle?

### 2. Semiperimeter that the triangle

The semiperimeter that the triangle is fifty percent its perimeter. The semiperimeter frequently shows up in formulas for triangles that it is given a separate name. By the triangle inequality, the longest side size of a triangle is less than the semiperimeter.

### 3. The triangle area using Heron's formula

Heron"s formula offers the area the a triangle once the size of all three sides is known. Over there is no should calculate angles or other distances in the triangle first. Heron"s formula functions equally well in all situations and species of triangles.

### 4. Calculate the heights that the triangle from its area.

There are many ways to uncover the elevation of the triangle. The easiest way is native the area and also base length. The area the a triangle is fifty percent of the product the the base"s length and height. Every next of the triangle can be a base; there are three bases and also three heights (altitudes). Triangle height is the perpendicular line segment native a vertex come a heat containing the base.

### 5. Calculate of the inner angle of the triangle utilizing a legislation of Cosines

The legislation of Cosines is useful for finding a triangle"s angles once we understand all 3 sides. The cosine rule, also known together the law of cosines, relates all 3 sides that a triangle through an edge of a triangle. The legislation of Cosines is the extrapolation of the Pythagorean theorem for any kind of triangle. Pythagorean organize works only in a ideal triangle. Pythagorean theorem is a special instance of the legislation of Cosines and also can be acquired from it since the cosine that 90° is 0. It is finest to discover the edge opposite the longest side first. V the law of Cosines, there is additionally no problem with obtuse angles as with the law of Sines since the cosine function is an adverse for obtuse angles, zero for right, and also positive because that acute angles. We additionally use train station cosine dubbed arccosine to identify the edge from cosine value.
a2=b2+c2−2bccos⁡α  α=arccos⁡(b2+c2−a22bc)=arccos⁡(122+132−522⋅ 12⋅ 13)=22∘37′11"  b2=a2+c2−2accos⁡β β=arccos⁡(a2+c2−b22ac)=arccos⁡(52+132−1222⋅ 5⋅ 13)=67∘22′49" γ=180∘−α−β=180∘−22∘37′11"−67∘22′49"=90∘ a2=b2+c2−2bccosα  α=arccos(2bcb2+c2−a2​)=arccos(2⋅ 12⋅ 13122+132−52​)=22∘37′11"  b2=a2+c2−2accosβ β=arccos(2aca2+c2−b2​)=arccos(2⋅ 5⋅ 1352+132−122​)=67∘22′49" γ=180∘−α−β=180∘−22∘37′11"−67∘22′49"=90∘

An incircle of a triangle is a circle i m sorry is tangent to every side. One incircle facility is referred to as an incenter and has a radius named inradius. All triangles have an incenter, and also it always lies within the triangle. The incenter is the intersection the the three-angle bisectors. The product that the inradius and also semiperimeter (half the perimeter) that a triangle is its area.

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