136 206 110 triangle

Obtuse scalene triangle.

Sides: a = 136   b = 206   c = 110

Area: T = 6869.411045505
Perimeter: p = 452
Semiperimeter: s = 226

Angle ∠ A = α = 37.32326470536° = 37°19'22″ = 0.65114030766 rad
Angle ∠ B = β = 113.311100629° = 113°18'40″ = 1.97876501385 rad
Angle ∠ C = γ = 29.36663466567° = 29°21'59″ = 0.51325394384 rad

Height: ha = 101.0210741986
Height: hb = 66.69333053889
Height: hc = 124.898837191

Median: ma = 150.4799234448
Median: mb = 68.47662732631
Median: mc = 165.6533252307

Inradius: r = 30.39656214825
Circumradius: R = 112.1555184938

Vertex coordinates: A[110; 0] B[0; 0] C[-53.81881818182; 124.898837191]
Centroid: CG[18.72772727273; 41.63327906367]
Coordinates of the circumscribed circle: U[55; 97.74334678555]
Coordinates of the inscribed circle: I[20; 30.39656214825]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6777352946° = 142°40'38″ = 0.65114030766 rad
∠ B' = β' = 66.68989937103° = 66°41'20″ = 1.97876501385 rad
∠ C' = γ' = 150.6343653343° = 150°38'1″ = 0.51325394384 rad

Calculate another triangle




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 136 ; ; b = 206 ; ; c = 110 ; ;

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

p = a+b+c = 136+206+110 = 452 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 452 }{ 2 } = 226 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 226 * (226-136)(226-206)(226-110) } ; ; T = sqrt{ 47188800 } = 6869.41 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6869.41 }{ 136 } = 101.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6869.41 }{ 206 } = 66.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6869.41 }{ 110 } = 124.9 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 206**2+110**2-136**2 }{ 2 * 206 * 110 } ) = 37° 19'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 136**2+110**2-206**2 }{ 2 * 136 * 110 } ) = 113° 18'40" ; ; gamma = 180° - alpha - beta = 180° - 37° 19'22" - 113° 18'40" = 29° 21'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6869.41 }{ 226 } = 30.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 136 }{ 2 * sin 37° 19'22" } = 112.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 206**2+2 * 110**2 - 136**2 } }{ 2 } = 150.479 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 110**2+2 * 136**2 - 206**2 } }{ 2 } = 68.476 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 206**2+2 * 136**2 - 110**2 } }{ 2 } = 165.653 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.