Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 125   b = 200   c = 119.1220203035

Area: T = 6996.023348618
Perimeter: p = 444.1220203036
Semiperimeter: s = 222.0660101518

Angle ∠ A = α = 35.96661995961° = 35°57'58″ = 0.62877286024 rad
Angle ∠ B = β = 110° = 1.92198621772 rad
Angle ∠ C = γ = 34.03438004039° = 34°2'2″ = 0.5944001874 rad

Height: ha = 111.9366375779
Height: hb = 69.96602348618
Height: hc = 117.4621577598

Median: ma = 152.2787908397
Median: mb = 70.05222047162
Median: mc = 155.7732572384

Inradius: r = 31.50550900111
Circumradius: R = 106.4187777248

Vertex coordinates: A[119.1220203035; 0] B[0; 0] C[-42.75325179157; 117.4621577598]
Centroid: CG[25.45658950399; 39.15438591994]
Coordinates of the circumscribed circle: U[59.56601015177; 88.18992148821]
Coordinates of the inscribed circle: I[22.06601015177; 31.50550900111]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.0343800404° = 144°2'2″ = 0.62877286024 rad
∠ B' = β' = 70° = 1.92198621772 rad
∠ C' = γ' = 145.9666199596° = 145°57'58″ = 0.5944001874 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 125 ; ; b = 200 ; ; beta = 110° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 200**2 = 125**2 + c**2 -2 * 200 * c * cos (110° ) ; ; ; ; c**2 +85.505c -24375 =0 ; ; p=1; q=85.5050358314; r=-24375 ; ; D = q**2 - 4pr = 85.505**2 - 4 * 1 * (-24375) = 104811.111153 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -85.51 ± sqrt{ 104811.11 } }{ 2 } ; ; c_{1,2} = -42.7525179157 ± 161.872720951 ; ;
c_{1} = 119.120203035 ; ; c_{2} = -204.625238867 ; ; ; ; (c -119.120203035) (c +204.625238867) = 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 = 125 ; ; b = 200 ; ; c = 119.12 ; ;

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

p = a+b+c = 125+200+119.12 = 444.12 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 444.12 }{ 2 } = 222.06 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 222.06 * (222.06-125)(222.06-200)(222.06-119.12) } ; ; T = sqrt{ 48944344.62 } = 6996.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6996.02 }{ 125 } = 111.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6996.02 }{ 200 } = 69.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6996.02 }{ 119.12 } = 117.46 ; ;

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{ 125**2-200**2-119.12**2 }{ 2 * 200 * 119.12 } ) = 35° 57'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 200**2-125**2-119.12**2 }{ 2 * 125 * 119.12 } ) = 110° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 119.12**2-125**2-200**2 }{ 2 * 200 * 125 } ) = 34° 2'2" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6996.02 }{ 222.06 } = 31.51 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 125 }{ 2 * sin 35° 57'58" } = 106.42 ; ;




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