Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 45   b = 60   c = 50

Area: T = 1100.97661294
Perimeter: p = 155
Semiperimeter: s = 77.5

Angle ∠ A = α = 47.22114422911° = 47°13'17″ = 0.82441696455 rad
Angle ∠ B = β = 78.13879773311° = 78°8'17″ = 1.36437649753 rad
Angle ∠ C = γ = 54.64105803778° = 54°38'26″ = 0.95436580328 rad

Height: ha = 48.93222724176
Height: hb = 36.69992043132
Height: hc = 44.03990451758

Median: ma = 50.43656025046
Median: mb = 36.91220576506
Median: mc = 46.77107173347

Inradius: r = 14.20661436051
Circumradius: R = 30.65546155715

Vertex coordinates: A[50; 0] B[0; 0] C[9.25; 44.03990451758]
Centroid: CG[19.75; 14.68796817253]
Coordinates of the circumscribed circle: U[25; 17.74399395668]
Coordinates of the inscribed circle: I[17.5; 14.20661436051]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.7798557709° = 132°46'43″ = 0.82441696455 rad
∠ B' = β' = 101.8622022669° = 101°51'43″ = 1.36437649753 rad
∠ C' = γ' = 125.3599419622° = 125°21'34″ = 0.95436580328 rad

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How did we calculate this triangle?

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

a = 45 ; ; b = 60 ; ; c = 50 ; ;

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

p = a+b+c = 45+60+50 = 155 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 155 }{ 2 } = 77.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 77.5 * (77.5-45)(77.5-60)(77.5-50) } ; ; T = sqrt{ 1212148.44 } = 1100.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1100.98 }{ 45 } = 48.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1100.98 }{ 60 } = 36.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1100.98 }{ 50 } = 44.04 ; ;

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{ 60**2+50**2-45**2 }{ 2 * 60 * 50 } ) = 47° 13'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45**2+50**2-60**2 }{ 2 * 45 * 50 } ) = 78° 8'17" ; ;
 gamma = 180° - alpha - beta = 180° - 47° 13'17" - 78° 8'17" = 54° 38'26" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1100.98 }{ 77.5 } = 14.21 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45 }{ 2 * sin 47° 13'17" } = 30.65 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 50**2 - 45**2 } }{ 2 } = 50.436 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 45**2 - 60**2 } }{ 2 } = 36.912 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 45**2 - 50**2 } }{ 2 } = 46.771 ; ;
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