Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 95   b = 125   c = 164.7199364311

Area: T = 5904.976590897
Perimeter: p = 384.7199364311
Semiperimeter: s = 192.3659682156

Angle ∠ A = α = 355.0001989677° = 35°1″ = 0.61108687108 rad
Angle ∠ B = β = 49° = 0.85552113335 rad
Angle ∠ C = γ = 965.9998010323° = 95°59'59″ = 1.67655126093 rad

Height: ha = 124.3155282294
Height: hb = 94.48796145435
Height: hc = 71.69774101212

Median: ma = 138.2844071713
Median: mb = 119.0488244378
Median: mc = 74.44438228143

Inradius: r = 30.69875757227
Circumradius: R = 82.81333120843

Vertex coordinates: A[164.7199364311; 0] B[0; 0] C[62.32656077541; 71.69774101212]
Centroid: CG[75.68216573552; 23.89991367071]
Coordinates of the circumscribed circle: U[82.36596821557; -8.65660622446]
Coordinates of the inscribed circle: I[67.36596821557; 30.69875757227]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1454.999801032° = 144°59'59″ = 0.61108687108 rad
∠ B' = β' = 131° = 0.85552113335 rad
∠ C' = γ' = 844.0001989677° = 84°1″ = 1.67655126093 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 95 ; ; b = 125 ; ; beta = 49° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 125**2 = 95**2 + c**2 -2 * 95 * c * cos (49° ) ; ; ; ; c**2 -124.651c -6600 =0 ; ; p=1; q=-124.651; r=-6600 ; ; D = q**2 - 4pr = 124.651**2 - 4 * 1 * (-6600) = 41937.9255277 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 124.65 ± sqrt{ 41937.93 } }{ 2 } ; ;
c_{1,2} = 62.32560775 ± 102.393756557 ; ; c_{1} = 164.719364311 ; ; c_{2} = -40.0681488032 ; ; ; ; text{ Factored form: } ; ; (c -164.719364311) (c +40.0681488032) = 0 ; ; ; ; c>0 ; ;
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 = 95 ; ; b = 125 ; ; c = 164.72 ; ;

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

p = a+b+c = 95+125+164.72 = 384.72 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 384.72 }{ 2 } = 192.36 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 192.36 * (192.36-95)(192.36-125)(192.36-164.72) } ; ; T = sqrt{ 34868740.49 } = 5904.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5904.98 }{ 95 } = 124.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5904.98 }{ 125 } = 94.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5904.98 }{ 164.72 } = 71.7 ; ;

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{ 125**2+164.72**2-95**2 }{ 2 * 125 * 164.72 } ) = 35° 1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 95**2+164.72**2-125**2 }{ 2 * 95 * 164.72 } ) = 49° ; ;
 gamma = 180° - alpha - beta = 180° - 35° 1" - 49° = 95° 59'59" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5904.98 }{ 192.36 } = 30.7 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 95 }{ 2 * sin 35° 1" } = 82.81 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 164.72**2 - 95**2 } }{ 2 } = 138.284 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 164.72**2+2 * 95**2 - 125**2 } }{ 2 } = 119.048 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 95**2 - 164.72**2 } }{ 2 } = 74.444 ; ;
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