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=3.4; b=3.19441125497; c=4.8 and a=3.4; b=3.59441125497; c=4.8.

#1 Obtuse scalene triangle.

Sides: a = 3.4   b = 3.19441125497   c = 4.8

Area: T = 5.4210588745
Perimeter: p = 11.39441125497
Semiperimeter: s = 5.69770562748

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 41.62877133166° = 41°37'40″ = 0.72765406575 rad
Angle ∠ C = γ = 93.37222866834° = 93°22'20″ = 1.63296538327 rad

Height: ha = 3.18985816147
Height: hb = 3.39441125497
Height: hc = 2.25985786438

Median: ma = 3.70655603476
Median: mb = 3.84404962251
Median: mc = 2.26330018758

Inradius: r = 0.95114718626
Circumradius: R = 2.4044163056

Vertex coordinates: A[4.8; 0] B[0; 0] C[2.54114213562; 2.25985786438]
Centroid: CG[2.44771404521; 0.75328595479]
Coordinates of the circumscribed circle: U[2.4; -0.14114213562]
Coordinates of the inscribed circle: I[2.50329437252; 0.95114718626]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 138.3722286683° = 138°22'20″ = 0.72765406575 rad
∠ C' = γ' = 86.62877133166° = 86°37'40″ = 1.63296538327 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 = 3.4 ; ; b = 3.19 ; ; c = 4.8 ; ;

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

p = a+b+c = 3.4+3.19+4.8 = 11.39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.39 }{ 2 } = 5.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.7 * (5.7-3.4)(5.7-3.19)(5.7-4.8) } ; ; T = sqrt{ 29.38 } = 5.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.42 }{ 3.4 } = 3.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.42 }{ 3.19 } = 3.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.42 }{ 4.8 } = 2.26 ; ;

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{ 3.4**2-3.19**2-4.8**2 }{ 2 * 3.19 * 4.8 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.19**2-3.4**2-4.8**2 }{ 2 * 3.4 * 4.8 } ) = 41° 37'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.8**2-3.4**2-3.19**2 }{ 2 * 3.19 * 3.4 } ) = 93° 22'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.42 }{ 5.7 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.4 }{ 2 * sin 45° } = 2.4 ; ;





#2 Acute scalene triangle.

Sides: a = 3.4   b = 3.59441125497   c = 4.8

Area: T = 6.0999411255
Perimeter: p = 11.79441125497
Semiperimeter: s = 5.89770562748

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 48.37222866834° = 48°22'20″ = 0.84442556693 rad
Angle ∠ C = γ = 86.62877133166° = 86°37'40″ = 1.51219388208 rad

Height: ha = 3.58878889735
Height: hb = 3.39441125497
Height: hc = 2.54114213562

Median: ma = 3.88444333576
Median: mb = 3.75110783443
Median: mc = 2.54553531209

Inradius: r = 1.03443145751
Circumradius: R = 2.4044163056

Vertex coordinates: A[4.8; 0] B[0; 0] C[2.25985786438; 2.54114213562]
Centroid: CG[2.35328595479; 0.84771404521]
Coordinates of the circumscribed circle: U[2.4; 0.14114213562]
Coordinates of the inscribed circle: I[2.30329437252; 1.03443145751]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 131.6287713317° = 131°37'40″ = 0.84442556693 rad
∠ C' = γ' = 93.37222866834° = 93°22'20″ = 1.51219388208 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 = 3.4 ; ; b = 3.59 ; ; c = 4.8 ; ;

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

p = a+b+c = 3.4+3.59+4.8 = 11.79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.79 }{ 2 } = 5.9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.9 * (5.9-3.4)(5.9-3.59)(5.9-4.8) } ; ; T = sqrt{ 37.2 } = 6.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.1 }{ 3.4 } = 3.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.1 }{ 3.59 } = 3.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.1 }{ 4.8 } = 2.54 ; ;

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{ 3.4**2-3.59**2-4.8**2 }{ 2 * 3.59 * 4.8 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.59**2-3.4**2-4.8**2 }{ 2 * 3.4 * 4.8 } ) = 48° 22'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.8**2-3.4**2-3.59**2 }{ 2 * 3.59 * 3.4 } ) = 86° 37'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.1 }{ 5.9 } = 1.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.4 }{ 2 * sin 45° } = 2.4 ; ; : Nr. 1




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