Triangle calculator

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

You have entered side a, c and angle α.

Triangle has two solutions: a=2.9; b=4.01219596489; c=6.2 and a=2.9; b=7.48551201477; c=6.2.

#1 Obtuse scalene triangle.

Sides: a = 2.9   b = 4.01219596489   c = 6.2

Area: T = 4.65990102647
Perimeter: p = 13.11219596489
Semiperimeter: s = 6.55659798245

Angle ∠ A = α = 22° = 0.38439724354 rad
Angle ∠ B = β = 31.21545114756° = 31°12'52″ = 0.54547959997 rad
Angle ∠ C = γ = 126.7855488524° = 126°47'8″ = 2.21328242185 rad

Height: ha = 3.21331105274
Height: hb = 2.32325608792
Height: hc = 1.5032906537

Median: ma = 5.01765137409
Median: mb = 4.40546617286
Median: mc = 1.62657029595

Inradius: r = 0.71106504885
Circumradius: R = 3.87107273857

Vertex coordinates: A[6.2; 0] B[0; 0] C[2.48801757883; 1.5032906537]
Centroid: CG[2.89333919294; 0.50109688457]
Coordinates of the circumscribed circle: U[3.1; -2.31878719754]
Coordinates of the inscribed circle: I[2.54440201755; 0.71106504885]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158° = 0.38439724354 rad
∠ B' = β' = 148.7855488524° = 148°47'8″ = 0.54547959997 rad
∠ C' = γ' = 53.21545114756° = 53°12'52″ = 2.21328242185 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 = 2.9 ; ; b = 4.01 ; ; c = 6.2 ; ;

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

p = a+b+c = 2.9+4.01+6.2 = 13.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.11 }{ 2 } = 6.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.56 * (6.56-2.9)(6.56-4.01)(6.56-6.2) } ; ; T = sqrt{ 21.71 } = 4.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.66 }{ 2.9 } = 3.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.66 }{ 4.01 } = 2.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.66 }{ 6.2 } = 1.5 ; ;

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{ 2.9**2-4.01**2-6.2**2 }{ 2 * 4.01 * 6.2 } ) = 22° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.01**2-2.9**2-6.2**2 }{ 2 * 2.9 * 6.2 } ) = 31° 12'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.2**2-2.9**2-4.01**2 }{ 2 * 4.01 * 2.9 } ) = 126° 47'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.66 }{ 6.56 } = 0.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.9 }{ 2 * sin 22° } = 3.87 ; ;





#2 Obtuse scalene triangle.

Sides: a = 2.9   b = 7.48551201477   c = 6.2

Area: T = 8.69223236155
Perimeter: p = 16.58551201477
Semiperimeter: s = 8.29325600738

Angle ∠ A = α = 22° = 0.38439724354 rad
Angle ∠ B = β = 104.7855488524° = 104°47'8″ = 1.82988517831 rad
Angle ∠ C = γ = 53.21545114756° = 53°12'52″ = 0.92987684351 rad

Height: ha = 5.99547059417
Height: hb = 2.32325608792
Height: hc = 2.80439753598

Median: ma = 6.71879618794
Median: mb = 3.06989157847
Median: mc = 4.75548408819

Inradius: r = 1.04882074942
Circumradius: R = 3.87107273857

Vertex coordinates: A[6.2; 0] B[0; 0] C[-0.74400825504; 2.80439753598]
Centroid: CG[1.82199724832; 0.93546584533]
Coordinates of the circumscribed circle: U[3.1; 2.31878719754]
Coordinates of the inscribed circle: I[0.80774399262; 1.04882074942]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158° = 0.38439724354 rad
∠ B' = β' = 75.21545114756° = 75°12'52″ = 1.82988517831 rad
∠ C' = γ' = 126.7855488524° = 126°47'8″ = 0.92987684351 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 = 2.9 ; ; b = 7.49 ; ; c = 6.2 ; ;

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

p = a+b+c = 2.9+7.49+6.2 = 16.59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.59 }{ 2 } = 8.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.29 * (8.29-2.9)(8.29-7.49)(8.29-6.2) } ; ; T = sqrt{ 75.56 } = 8.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.69 }{ 2.9 } = 5.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.69 }{ 7.49 } = 2.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.69 }{ 6.2 } = 2.8 ; ;

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{ 2.9**2-7.49**2-6.2**2 }{ 2 * 7.49 * 6.2 } ) = 22° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.49**2-2.9**2-6.2**2 }{ 2 * 2.9 * 6.2 } ) = 104° 47'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.2**2-2.9**2-7.49**2 }{ 2 * 7.49 * 2.9 } ) = 53° 12'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.69 }{ 8.29 } = 1.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.9 }{ 2 * sin 22° } = 3.87 ; ; : Nr. 1




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