Triangle calculator

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

You have entered side c, angle α and angle β.

Right scalene triangle.

Sides: a = 2.87991632528   b = 1.10218080759   c = 2.66

Area: T = 1.4655404741
Perimeter: p = 6.64109713287
Semiperimeter: s = 3.32204856643

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 22.5° = 22°30' = 0.39326990817 rad
Angle ∠ C = γ = 67.5° = 67°30' = 1.17880972451 rad

Height: ha = 1.01879379301
Height: hb = 2.66
Height: hc = 1.10218080759

Median: ma = 1.44395816264
Median: mb = 2.71664490165
Median: mc = 1.72771019183

Inradius: r = 0.44113224116
Circumradius: R = 1.44395816264

Vertex coordinates: A[2.66; 0] B[0; 0] C[2.66; 1.10218080759]
Centroid: CG[1.77333333333; 0.36772693586]
Coordinates of the circumscribed circle: U[1.33; 0.5510904038]
Coordinates of the inscribed circle: I[2.21986775884; 0.44113224116]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 157.5° = 157°30' = 0.39326990817 rad
∠ C' = γ' = 112.5° = 112°30' = 1.17880972451 rad

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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 = 2.88 ; ; b = 1.1 ; ; c = 2.66 ; ;

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

p = a+b+c = 2.88+1.1+2.66 = 6.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.64 }{ 2 } = 3.32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.32 * (3.32-2.88)(3.32-1.1)(3.32-2.66) } ; ; T = sqrt{ 2.15 } = 1.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.47 }{ 2.88 } = 1.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.47 }{ 1.1 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.47 }{ 2.66 } = 1.1 ; ;

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{ 2.88**2-1.1**2-2.66**2 }{ 2 * 1.1 * 2.66 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.1**2-2.88**2-2.66**2 }{ 2 * 2.88 * 2.66 } ) = 22° 30' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.66**2-2.88**2-1.1**2 }{ 2 * 1.1 * 2.88 } ) = 67° 30' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.47 }{ 3.32 } = 0.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.88 }{ 2 * sin 90° } = 1.44 ; ;




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