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=984.2; b=4000; c=3241.957731666 and a=984.2; b=4000; c=4636.505470744.

#1 Obtuse scalene triangle.

Sides: a = 984.2   b = 4000   c = 3241.957731666

Area: T = 1125919.966022
Perimeter: p = 8226.157731666
Semiperimeter: s = 4113.079865833

Angle ∠ A = α = 10° = 0.17545329252 rad
Angle ∠ B = β = 135.1110361827° = 135°6'37″ = 2.35881206674 rad
Angle ∠ C = γ = 34.89896381728° = 34°53'23″ = 0.60989390609 rad

Height: ha = 2287.999016505
Height: hb = 562.9659980111
Height: hc = 694.5932710668

Median: ma = 3607.351099644
Median: mb = 1318.889909371
Median: mc = 2420.07329347

Inradius: r = 273.7411412152
Circumradius: R = 2833.891095476

Vertex coordinates: A[3241.957731666; 0] B[0; 0] C[-697.2743695393; 694.5932710668]
Centroid: CG[848.2287873754; 231.5310903556]
Coordinates of the circumscribed circle: U[1620.979865833; 2324.514417132]
Coordinates of the inscribed circle: I[113.0798658328; 273.7411412152]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170° = 0.17545329252 rad
∠ B' = β' = 44.89896381728° = 44°53'23″ = 2.35881206674 rad
∠ C' = γ' = 145.1110361827° = 145°6'37″ = 0.60989390609 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 = 984.2 ; ; b = 4000 ; ; c = 3241.96 ; ;

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

p = a+b+c = 984.2+4000+3241.96 = 8226.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8226.16 }{ 2 } = 4113.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4113.08 * (4113.08-984.2)(4113.08-4000)(4113.08-3241.96) } ; ; T = sqrt{ 1.268 * 10**{ 12 } } = 1125919.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1125919.96 }{ 984.2 } = 2287.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1125919.96 }{ 4000 } = 562.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1125919.96 }{ 3241.96 } = 694.59 ; ;

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{ 984.2**2-4000**2-3241.96**2 }{ 2 * 4000 * 3241.96 } ) = 10° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4000**2-984.2**2-3241.96**2 }{ 2 * 984.2 * 3241.96 } ) = 135° 6'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3241.96**2-984.2**2-4000**2 }{ 2 * 4000 * 984.2 } ) = 34° 53'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1125919.96 }{ 4113.08 } = 273.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 984.2 }{ 2 * sin 10° } = 2833.89 ; ;





#2 Obtuse scalene triangle.

Sides: a = 984.2   b = 4000   c = 4636.505470744

Area: T = 1610241.186638
Perimeter: p = 9620.705470744
Semiperimeter: s = 4810.352235372

Angle ∠ A = α = 10° = 0.17545329252 rad
Angle ∠ B = β = 44.89896381728° = 44°53'23″ = 0.78334719861 rad
Angle ∠ C = γ = 125.1110361827° = 125°6'37″ = 2.18435877422 rad

Height: ha = 3272.183286199
Height: hb = 805.1210593192
Height: hc = 694.5932710668

Median: ma = 4301.910952265
Median: mb = 2689.408751302
Median: mc = 1763.528795398

Inradius: r = 334.7454955874
Circumradius: R = 2833.891095476

Vertex coordinates: A[4636.505470744; 0] B[0; 0] C[697.2743695393; 694.5932710668]
Centroid: CG[1777.926613428; 231.5310903556]
Coordinates of the circumscribed circle: U[2318.252235372; -1629.921146066]
Coordinates of the inscribed circle: I[810.3522353721; 334.7454955874]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170° = 0.17545329252 rad
∠ B' = β' = 135.1110361827° = 135°6'37″ = 0.78334719861 rad
∠ C' = γ' = 54.89896381728° = 54°53'23″ = 2.18435877422 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 = 984.2 ; ; b = 4000 ; ; c = 4636.5 ; ;

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

p = a+b+c = 984.2+4000+4636.5 = 9620.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9620.7 }{ 2 } = 4810.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4810.35 * (4810.35-984.2)(4810.35-4000)(4810.35-4636.5) } ; ; T = sqrt{ 2.593 * 10**{ 12 } } = 1610241.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1610241.19 }{ 984.2 } = 3272.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1610241.19 }{ 4000 } = 805.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1610241.19 }{ 4636.5 } = 694.59 ; ;

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{ 984.2**2-4000**2-4636.5**2 }{ 2 * 4000 * 4636.5 } ) = 10° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4000**2-984.2**2-4636.5**2 }{ 2 * 984.2 * 4636.5 } ) = 44° 53'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4636.5**2-984.2**2-4000**2 }{ 2 * 4000 * 984.2 } ) = 125° 6'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1610241.19 }{ 4810.35 } = 334.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 984.2 }{ 2 * sin 10° } = 2833.89 ; ; : Nr. 1




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