Triangle calculator

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

You have entered median ma, median mb and median mc.

Acute scalene triangle.

Sides: a = 5.69660024969   b = 4.80774017006   c = 3.33333333333

Area: T = 8
Perimeter: p = 13.83767375308
Semiperimeter: s = 6.91883687654

Angle ∠ A = α = 86.82201698801° = 86°49'13″ = 1.51552978215 rad
Angle ∠ B = β = 57.42659428654° = 57°25'33″ = 1.00222717791 rad
Angle ∠ C = γ = 35.75438872544° = 35°45'14″ = 0.6244023053 rad

Height: ha = 2.80989875327
Height: hb = 3.32882011774
Height: hc = 4.8

Median: ma = 3
Median: mb = 4
Median: mc = 5

Inradius: r = 1.15663419458
Circumradius: R = 2.85223929261

Vertex coordinates: A[3.33333333333; 0] B[0; 0] C[3.06766666667; 4.8]
Centroid: CG[2.13333333333; 1.6]
Coordinates of the circumscribed circle: U[1.66766666667; 2.31548148148]
Coordinates of the inscribed circle: I[2.11109670648; 1.15663419458]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 93.18798301199° = 93°10'47″ = 1.51552978215 rad
∠ B' = β' = 122.5744057135° = 122°34'27″ = 1.00222717791 rad
∠ C' = γ' = 144.2466112746° = 144°14'46″ = 0.6244023053 rad

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How did we calculate this triangle?

1. Input data entered: median ma, median mb and median mc.

ma = 3 ; ; mb = 4 ; ; mc = 5 ; ;


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 = 5.7 ; ; b = 4.81 ; ; c = 3.33 ; ;

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

p = a+b+c = 5.7+4.81+3.33 = 13.84 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.84 }{ 2 } = 6.92 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.92 * (6.92-5.7)(6.92-4.81)(6.92-3.33) } ; ; T = sqrt{ 64 } = 8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8 }{ 5.7 } = 2.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8 }{ 4.81 } = 3.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8 }{ 3.33 } = 4.8 ; ;

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{ 5.7**2-4.81**2-3.33**2 }{ 2 * 4.81 * 3.33 } ) = 86° 49'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.81**2-5.7**2-3.33**2 }{ 2 * 5.7 * 3.33 } ) = 57° 25'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.33**2-5.7**2-4.81**2 }{ 2 * 4.81 * 5.7 } ) = 35° 45'14" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8 }{ 6.92 } = 1.16 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.7 }{ 2 * sin 86° 49'13" } = 2.85 ; ;




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