Triangle calculator - result

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side b, c and median ma.

Obtuse scalene triangle.

Sides: a = 4.06220192023   b = 2.5   c = 2

Area: T = 1.95215618745
Perimeter: p = 8.56220192023
Semiperimeter: s = 4.28110096012

Angle ∠ A = α = 128.6822187453° = 128°40'56″ = 2.24659278597 rad
Angle ∠ B = β = 28.71442293977° = 28°42'51″ = 0.50111578452 rad
Angle ∠ C = γ = 22.60435831488° = 22°36'13″ = 0.39545069487 rad

Height: ha = 0.96108826435
Height: hb = 1.56112494996
Height: hc = 1.95215618745

Median: ma = 1
Median: mb = 2.94774565306
Median: mc = 3.22110246817

Inradius: r = 0.45658648675
Circumradius: R = 2.60217745424

Vertex coordinates: A[2; 0] B[0; 0] C[3.56325; 1.95215618745]
Centroid: CG[1.85441666667; 0.65105206248]
Coordinates of the circumscribed circle: U[1; 2.40219223071]
Coordinates of the inscribed circle: I[1.78110096012; 0.45658648675]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 51.31878125465° = 51°19'4″ = 2.24659278597 rad
∠ B' = β' = 151.2865770602° = 151°17'9″ = 0.50111578452 rad
∠ C' = γ' = 157.3966416851° = 157°23'47″ = 0.39545069487 rad

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How did we calculate this triangle?

1. Input data entered: side b, c and median ma.

b = 2.5 ; ; c = 2 ; ; ma = 1 ; ;


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 = 4.06 ; ; b = 2.5 ; ; c = 2 ; ;

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

p = a+b+c = 4.06+2.5+2 = 8.56 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.56 }{ 2 } = 4.28 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.28 * (4.28-4.06)(4.28-2.5)(4.28-2) } ; ; T = sqrt{ 3.81 } = 1.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.95 }{ 4.06 } = 0.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.95 }{ 2.5 } = 1.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.95 }{ 2 } = 1.95 ; ;

6. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 4.06**2-2.5**2-2**2 }{ 2 * 2.5 * 2 } ) = 128° 40'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-4.06**2-2**2 }{ 2 * 4.06 * 2 } ) = 28° 42'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2**2-4.06**2-2.5**2 }{ 2 * 2.5 * 4.06 } ) = 22° 36'13" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.95 }{ 4.28 } = 0.46 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.06 }{ 2 * sin 128° 40'56" } = 2.6 ; ;




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