Triangle calculator

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

You have entered side a, angle α and angle γ.

Right scalene triangle.

Sides: a = 180   b = 98.03550263027   c = 150.961070223

Area: T = 7399.718820691
Perimeter: p = 428.9965728533
Semiperimeter: s = 214.4987864266

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 33° = 0.57659586532 rad
Angle ∠ C = γ = 57° = 0.99548376736 rad

Height: ha = 82.21990911878
Height: hb = 150.961070223
Height: hc = 98.03550263027

Median: ma = 90
Median: mb = 158.7199407173
Median: mc = 123.7266107943

Inradius: r = 34.49878642664
Circumradius: R = 90

Vertex coordinates: A[150.961070223; 0] B[0; 0] C[150.961070223; 98.03550263027]
Centroid: CG[100.6440468153; 32.67883421009]
Coordinates of the circumscribed circle: U[75.48803511151; 49.01875131514]
Coordinates of the inscribed circle: I[116.4632837964; 34.49878642664]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 147° = 0.57659586532 rad
∠ C' = γ' = 123° = 0.99548376736 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 = 180 ; ; b = 98.04 ; ; c = 150.96 ; ;

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

p = a+b+c = 180+98.04+150.96 = 429 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 429 }{ 2 } = 214.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 214.5 * (214.5-180)(214.5-98.04)(214.5-150.96) } ; ; T = sqrt{ 54755829.54 } = 7399.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7399.72 }{ 180 } = 82.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7399.72 }{ 98.04 } = 150.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7399.72 }{ 150.96 } = 98.04 ; ;

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{ 180**2-98.04**2-150.96**2 }{ 2 * 98.04 * 150.96 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 98.04**2-180**2-150.96**2 }{ 2 * 180 * 150.96 } ) = 33° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 150.96**2-180**2-98.04**2 }{ 2 * 98.04 * 180 } ) = 57° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7399.72 }{ 214.5 } = 34.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 180 }{ 2 * sin 90° } = 90 ; ;




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