Triangle calculator

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

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 6.312   b = 6.312   c = 7.705

Area: T = 19.262234118
Perimeter: p = 20.329
Semiperimeter: s = 10.16545

Angle ∠ A = α = 52.38655200632° = 52°23'8″ = 0.91442998055 rad
Angle ∠ B = β = 52.38655200632° = 52°23'8″ = 0.91442998055 rad
Angle ∠ C = γ = 75.22989598735° = 75°13'44″ = 1.31329930426 rad

Height: ha = 6.10334034157
Height: hb = 6.10334034157
Height: hc = 54.9999587748

Median: ma = 6.29663361171
Median: mb = 6.29663361171
Median: mc = 54.9999587748

Inradius: r = 1.89550603748
Circumradius: R = 3.98441672496

Vertex coordinates: A[7.705; 0] B[0; 0] C[3.85325; 54.9999587748]
Centroid: CG[3.85325; 1.66766529249]
Coordinates of the circumscribed circle: U[3.85325; 1.01657915252]
Coordinates of the inscribed circle: I[3.85325; 1.89550603748]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.6144479937° = 127°36'52″ = 0.91442998055 rad
∠ B' = β' = 127.6144479937° = 127°36'52″ = 0.91442998055 rad
∠ C' = γ' = 104.7711040126° = 104°46'16″ = 1.31329930426 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 6.312 ; ; b = 6.312 ; ; c = 7.705 ; ;

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

p = a+b+c = 6.31+6.31+7.71 = 20.33 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.33 }{ 2 } = 10.16 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.16 * (10.16-6.31)(10.16-6.31)(10.16-7.71) } ; ; T = sqrt{ 371.04 } = 19.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.26 }{ 6.31 } = 6.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.26 }{ 6.31 } = 6.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.26 }{ 7.71 } = 5 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 6.31**2+7.71**2-6.31**2 }{ 2 * 6.31 * 7.71 } ) = 52° 23'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.31**2+7.71**2-6.31**2 }{ 2 * 6.31 * 7.71 } ) = 52° 23'8" ; ;
 gamma = 180° - alpha - beta = 180° - 52° 23'8" - 52° 23'8" = 75° 13'44" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.26 }{ 10.16 } = 1.9 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.31 }{ 2 * sin 52° 23'8" } = 3.98 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.31**2+2 * 7.71**2 - 6.31**2 } }{ 2 } = 6.296 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.71**2+2 * 6.31**2 - 6.31**2 } }{ 2 } = 6.296 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.31**2+2 * 6.31**2 - 7.71**2 } }{ 2 } = 5 ; ;
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