Triangle calculator

You have entered side b, c and angle α.

Right scalene triangle.

Sides: a = 145.7899471499 b = 111.1 c = 94.4

Area: T = 5243.92
Perimeter: p = 351.2899471499
Semiperimeter: s = 175.645473575

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 49.64659439969° = 49°38'45″ = 0.8666485183 rad
Angle ∠ C = γ = 40.35440560031° = 40°21'15″ = 0.70443111438 rad

Height: h_a = 71.93882537858
Height: h_b = 94.4
Height: h_c = 111.1

Median: m_a = 72.89547357496
Median: m_b = 109.5321559379
Median: m_c = 120.7110604339

Inradius: r = 29.85552642504
Circumradius: R = 72.89547357496

Vertex coordinates: A[94.4; 0] B[0; 0] C[94.4; 111.1]
Centroid: CG[62.93333333333; 37.03333333333]
Coordinates of the circumscribed circle: U[47.2; 55.55]
Coordinates of the inscribed circle: I[64.54547357496; 29.85552642504]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 130.3544056003° = 130°21'15″ = 0.8666485183 rad
∠ C' = γ' = 139.6465943997° = 139°38'45″ = 0.70443111438 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.

$a = 145.79 ; ; b = 111.1 ; ; c = 94.4 ; ;$

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

$p = a+b+c = 145.79+111.1+94.4 = 351.29 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 351.29 }{ 2 } = 175.64 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 175.64 * (175.64-145.79)(175.64-111.1)(175.64-94.4) } ; ; T = sqrt{ 27498696.97 } = 5243.92 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5243.92 }{ 145.79 } = 71.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5243.92 }{ 111.1 } = 94.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5243.92 }{ 94.4 } = 111.1 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 145.79**2-111.1**2-94.4**2 }{ 2 * 111.1 * 94.4 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 111.1**2-145.79**2-94.4**2 }{ 2 * 145.79 * 94.4 } ) = 49° 38'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 94.4**2-145.79**2-111.1**2 }{ 2 * 111.1 * 145.79 } ) = 40° 21'15" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 5243.92 }{ 175.64 } = 29.86 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 145.79 }{ 2 * sin 90° } = 72.89 ; ;$

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