Triangle calculator SSA

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Triangle has two solutions with side c=63.52334994295 and with side c=11.08325128704

#1 Obtuse scalene triangle.

Sides: a = 48   b = 40   c = 63.52334994295

Area: T = 959.4399204043
Perimeter: p = 151.5233499429
Semiperimeter: s = 75.76217497147

Angle ∠ A = α = 49.04114908974° = 49°2'29″ = 0.85659354862 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 91.95985091026° = 91°57'31″ = 1.60549787591 rad

Height: ha = 39.97766335018
Height: hb = 47.97219602022
Height: hc = 30.20773787704

Median: ma = 47.34657230369
Median: mb = 52.62771554417
Median: mc = 30.71114189685

Inradius: r = 12.66438997602
Circumradius: R = 31.78803145813

Vertex coordinates: A[63.52334994295; 0] B[0; 0] C[37.30330061499; 30.20773787704]
Centroid: CG[33.60988351931; 10.06991262568]
Coordinates of the circumscribed circle: U[31.76217497147; -1.08661169117]
Coordinates of the inscribed circle: I[35.76217497147; 12.66438997602]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.9598509103° = 130°57'31″ = 0.85659354862 rad
∠ B' = β' = 141° = 0.68106784083 rad
∠ C' = γ' = 88.04114908974° = 88°2'29″ = 1.60549787591 rad




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 = 48 ; ; b = 40 ; ; c = 63.52 ; ;

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

p = a+b+c = 48+40+63.52 = 151.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 151.52 }{ 2 } = 75.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 75.76 * (75.76-48)(75.76-40)(75.76-63.52) } ; ; T = sqrt{ 920523.59 } = 959.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 959.44 }{ 48 } = 39.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 959.44 }{ 40 } = 47.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 959.44 }{ 63.52 } = 30.21 ; ;

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{ 48**2-40**2-63.52**2 }{ 2 * 40 * 63.52 } ) = 49° 2'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-48**2-63.52**2 }{ 2 * 48 * 63.52 } ) = 39° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 63.52**2-48**2-40**2 }{ 2 * 40 * 48 } ) = 91° 57'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 959.44 }{ 75.76 } = 12.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48 }{ 2 * sin 49° 2'29" } = 31.78 ; ;





#2 Obtuse scalene triangle.

Sides: a = 48   b = 40   c = 11.08325128704

Area: T = 167.3876832002
Perimeter: p = 99.08325128704
Semiperimeter: s = 49.54112564352

Angle ∠ A = α = 130.9598509103° = 130°57'31″ = 2.28656571673 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 10.04114908974° = 10°2'29″ = 0.1755257078 rad

Height: ha = 6.97444513334
Height: hb = 8.36993416001
Height: hc = 30.20773787704

Median: ma = 16.89441127545
Median: mb = 28.522036195
Median: mc = 43.83325732432

Inradius: r = 3.3798736109
Circumradius: R = 31.78803145813

Vertex coordinates: A[11.08325128704; 0] B[0; 0] C[37.30330061499; 30.20773787704]
Centroid: CG[16.12985063401; 10.06991262568]
Coordinates of the circumscribed circle: U[5.54112564352; 31.29334956821]
Coordinates of the inscribed circle: I[9.54112564352; 3.3798736109]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 49.04114908974° = 49°2'29″ = 2.28656571673 rad
∠ B' = β' = 141° = 0.68106784083 rad
∠ C' = γ' = 169.9598509103° = 169°57'31″ = 0.1755257078 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 48 ; ; b = 40 ; ; beta = 39° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 40**2 = 48**2 + c**2 -2 * 40 * c * cos (39° ) ; ; ; ; c**2 -74.606c +704 =0 ; ; p=1; q=-74.6060122999; r=704 ; ; D = q**2 - 4pr = 74.606**2 - 4 * 1 * 704 = 2750.05707129 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 74.61 ± sqrt{ 2750.06 } }{ 2 } ; ; c_{1,2} = 37.3030061499 ± 26.2204932795 ; ; c_{1} = 63.5234994295 ; ;
c_{2} = 11.0825128704 ; ; ; ; (c -63.5234994295) (c -11.0825128704) = 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 = 48 ; ; b = 40 ; ; c = 11.08 ; ;

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

p = a+b+c = 48+40+11.08 = 99.08 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 99.08 }{ 2 } = 49.54 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 49.54 * (49.54-48)(49.54-40)(49.54-11.08) } ; ; T = sqrt{ 28018.35 } = 167.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 167.39 }{ 48 } = 6.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 167.39 }{ 40 } = 8.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 167.39 }{ 11.08 } = 30.21 ; ;

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{ 48**2-40**2-11.08**2 }{ 2 * 40 * 11.08 } ) = 130° 57'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-48**2-11.08**2 }{ 2 * 48 * 11.08 } ) = 39° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.08**2-48**2-40**2 }{ 2 * 40 * 48 } ) = 10° 2'29" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 167.39 }{ 49.54 } = 3.38 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48 }{ 2 * sin 130° 57'31" } = 31.78 ; ;




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