Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Obtuse isosceles triangle.

Sides: a = 245.25   b = 245.25   c = 437.8133343951

Area: T = 24206.21999912
Perimeter: p = 928.3133343951
Semiperimeter: s = 464.1576671975

Angle ∠ A = α = 26.8° = 26°48' = 0.46877482395 rad
Angle ∠ B = β = 26.8° = 26°48' = 0.46877482395 rad
Angle ∠ C = γ = 126.4° = 126°24' = 2.20660961745 rad

Height: ha = 197.4400203801
Height: hb = 197.4400203801
Height: hc = 110.5787716854

Median: ma = 332.982221078
Median: mb = 332.982221078
Median: mc = 110.5787716854

Inradius: r = 52.15109254368
Circumradius: R = 271.9769634621

Vertex coordinates: A[437.8133343951; 0] B[0; 0] C[218.9076671975; 110.5787716854]
Centroid: CG[218.9076671975; 36.85992389514]
Coordinates of the circumscribed circle: U[218.9076671975; -161.3921917767]
Coordinates of the inscribed circle: I[218.9076671975; 52.15109254368]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.2° = 153°12' = 0.46877482395 rad
∠ B' = β' = 153.2° = 153°12' = 0.46877482395 rad
∠ C' = γ' = 53.6° = 53°36' = 2.20660961745 rad

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How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 245.25 ; ; b = 245.25 ; ; gamma = 126° 24' ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 245.25**2+245.25**2 - 2 * 245.25 * 245.25 * cos(126° 24') } ; ; c = 437.81 ; ;


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 = 245.25 ; ; b = 245.25 ; ; c = 437.81 ; ;

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

p = a+b+c = 245.25+245.25+437.81 = 928.31 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 928.31 }{ 2 } = 464.16 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 464.16 * (464.16-245.25)(464.16-245.25)(464.16-437.81) } ; ; T = sqrt{ 585940118.01 } = 24206.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24206.2 }{ 245.25 } = 197.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24206.2 }{ 245.25 } = 197.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24206.2 }{ 437.81 } = 110.58 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 245.25**2-245.25**2-437.81**2 }{ 2 * 245.25 * 437.81 } ) = 26° 48' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 245.25**2-245.25**2-437.81**2 }{ 2 * 245.25 * 437.81 } ) = 26° 48' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 437.81**2-245.25**2-245.25**2 }{ 2 * 245.25 * 245.25 } ) = 126° 24' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24206.2 }{ 464.16 } = 52.15 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 245.25 }{ 2 * sin 26° 48' } = 271.97 ; ;




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