Triangle calculator

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

You have entered side a, b and angle α.

Triangle has two solutions: a=115; b=250; c=181.166645455 and a=115; b=250; c=271.9877438969.

#1 Obtuse scalene triangle.

Sides: a = 115   b = 250   c = 181.166645455

Area: T = 9570.532151344
Perimeter: p = 546.166645455
Semiperimeter: s = 273.0833227275

Angle ∠ A = α = 25° = 0.4366332313 rad
Angle ∠ B = β = 113.2588106349° = 113°15'29″ = 1.97767268604 rad
Angle ∠ C = γ = 41.74218936505° = 41°44'31″ = 0.72985334802 rad

Height: ha = 166.4444026321
Height: hb = 76.56442521075
Height: hc = 105.6554565435

Median: ma = 210.6054824558
Median: mb = 86.01224533254
Median: mc = 172.2132598077

Inradius: r = 35.04662077402
Circumradius: R = 136.0576591031

Vertex coordinates: A[181.166645455; 0] B[0; 0] C[-45.41104922094; 105.6554565435]
Centroid: CG[45.25219874468; 35.21881884784]
Coordinates of the circumscribed circle: U[90.58332272749; 101.5198840121]
Coordinates of the inscribed circle: I[23.08332272749; 35.04662077402]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155° = 0.4366332313 rad
∠ B' = β' = 66.74218936505° = 66°44'31″ = 1.97767268604 rad
∠ C' = γ' = 138.2588106349° = 138°15'29″ = 0.72985334802 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 = 115 ; ; b = 250 ; ; c = 181.17 ; ;

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

p = a+b+c = 115+250+181.17 = 546.17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 546.17 }{ 2 } = 273.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 273.08 * (273.08-115)(273.08-250)(273.08-181.17) } ; ; T = sqrt{ 91595073.45 } = 9570.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9570.53 }{ 115 } = 166.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9570.53 }{ 250 } = 76.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9570.53 }{ 181.17 } = 105.65 ; ;

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{ 115**2-250**2-181.17**2 }{ 2 * 250 * 181.17 } ) = 25° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 250**2-115**2-181.17**2 }{ 2 * 115 * 181.17 } ) = 113° 15'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 181.17**2-115**2-250**2 }{ 2 * 250 * 115 } ) = 41° 44'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9570.53 }{ 273.08 } = 35.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 115 }{ 2 * sin 25° } = 136.06 ; ;





#2 Acute scalene triangle.

Sides: a = 115   b = 250   c = 271.9877438969

Area: T = 14368.3577334
Perimeter: p = 636.9877438969
Semiperimeter: s = 318.4943719484

Angle ∠ A = α = 25° = 0.4366332313 rad
Angle ∠ B = β = 66.74218936505° = 66°44'31″ = 1.16548657932 rad
Angle ∠ C = γ = 88.25881063495° = 88°15'29″ = 1.54403945474 rad

Height: ha = 249.8844475374
Height: hb = 114.9476858672
Height: hc = 105.6554565435

Median: ma = 254.8188236157
Median: mb = 167.2610525763
Median: mc = 139.1769710285

Inradius: r = 45.1133471491
Circumradius: R = 136.0576591031

Vertex coordinates: A[271.9877438969; 0] B[0; 0] C[45.41104922094; 105.6554565435]
Centroid: CG[105.7999310393; 35.21881884784]
Coordinates of the circumscribed circle: U[135.9943719484; 4.13657253141]
Coordinates of the inscribed circle: I[68.49437194843; 45.1133471491]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155° = 0.4366332313 rad
∠ B' = β' = 113.2588106349° = 113°15'29″ = 1.16548657932 rad
∠ C' = γ' = 91.74218936505° = 91°44'31″ = 1.54403945474 rad

Calculate another triangle

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 = 115 ; ; b = 250 ; ; c = 271.99 ; ;

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

p = a+b+c = 115+250+271.99 = 636.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 636.99 }{ 2 } = 318.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 318.49 * (318.49-115)(318.49-250)(318.49-271.99) } ; ; T = sqrt{ 206449692.48 } = 14368.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14368.36 }{ 115 } = 249.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14368.36 }{ 250 } = 114.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14368.36 }{ 271.99 } = 105.65 ; ;

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{ 115**2-250**2-271.99**2 }{ 2 * 250 * 271.99 } ) = 25° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 250**2-115**2-271.99**2 }{ 2 * 115 * 271.99 } ) = 66° 44'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 271.99**2-115**2-250**2 }{ 2 * 250 * 115 } ) = 88° 15'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14368.36 }{ 318.49 } = 45.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 115 }{ 2 * sin 25° } = 136.06 ; ; : Nr. 1




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