Triangle calculator

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

You have entered side b, c and angle γ.

Triangle has two solutions: a=1.05436078092; b=2.4; c=1.5 and a=3.33114103874; b=2.4; c=1.5.

#1 Obtuse scalene triangle.

Sides: a = 1.05436078092   b = 2.4   c = 1.5

Area: T = 0.51442490841
Perimeter: p = 4.95436078092
Semiperimeter: s = 2.47768039046

Angle ∠ A = α = 16.66003329111° = 16°36'1″ = 0.29897304662 rad
Angle ∠ B = β = 139.4399667089° = 139°23'59″ = 2.43329831669 rad
Angle ∠ C = γ = 24° = 0.41988790205 rad

Height: ha = 0.97661679434
Height: hb = 0.42985409034
Height: hc = 0.68656654455

Median: ma = 1.93106676685
Median: mb = 0.49899435762
Median: mc = 1.6954858315

Inradius: r = 0.20876260794
Circumradius: R = 1.84439450017

Vertex coordinates: A[1.5; 0] B[0; 0] C[-0.87999701948; 0.68656654455]
Centroid: CG[0.23333432684; 0.22985551485]
Coordinates of the circumscribed circle: U[0.75; 1.68545275804]
Coordinates of the inscribed circle: I[0.07768039046; 0.20876260794]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.4399667089° = 163°23'59″ = 0.29897304662 rad
∠ B' = β' = 40.66003329111° = 40°36'1″ = 2.43329831669 rad
∠ C' = γ' = 156° = 0.41988790205 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 = 1.05 ; ; b = 2.4 ; ; c = 1.5 ; ;

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

p = a+b+c = 1.05+2.4+1.5 = 4.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4.95 }{ 2 } = 2.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.48 * (2.48-1.05)(2.48-2.4)(2.48-1.5) } ; ; T = sqrt{ 0.26 } = 0.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.51 }{ 1.05 } = 0.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.51 }{ 2.4 } = 0.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.51 }{ 1.5 } = 0.69 ; ;

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{ 1.05**2-2.4**2-1.5**2 }{ 2 * 2.4 * 1.5 } ) = 16° 36'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.4**2-1.05**2-1.5**2 }{ 2 * 1.05 * 1.5 } ) = 139° 23'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.5**2-1.05**2-2.4**2 }{ 2 * 2.4 * 1.05 } ) = 24° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.51 }{ 2.48 } = 0.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.05 }{ 2 * sin 16° 36'1" } = 1.84 ; ;





#2 Obtuse scalene triangle.

Sides: a = 3.33114103874   b = 2.4   c = 1.5

Area: T = 1.62660080132
Perimeter: p = 7.23114103874
Semiperimeter: s = 3.61657051937

Angle ∠ A = α = 115.4399667089° = 115°23'59″ = 2.01441041464 rad
Angle ∠ B = β = 40.66003329111° = 40°36'1″ = 0.70986094867 rad
Angle ∠ C = γ = 24° = 0.41988790205 rad

Height: ha = 0.97661679434
Height: hb = 1.35550066777
Height: hc = 2.16880106843

Median: ma = 1.10992457832
Median: mb = 2.28878259516
Median: mc = 2.80547544607

Inradius: r = 0.45497070215
Circumradius: R = 1.84439450017

Vertex coordinates: A[1.5; 0] B[0; 0] C[2.52994317232; 2.16880106843]
Centroid: CG[1.34331439077; 0.72326702281]
Coordinates of the circumscribed circle: U[0.75; 1.68545275804]
Coordinates of the inscribed circle: I[1.21657051937; 0.45497070215]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 64.66003329111° = 64°36'1″ = 2.01441041464 rad
∠ B' = β' = 139.4399667089° = 139°23'59″ = 0.70986094867 rad
∠ C' = γ' = 156° = 0.41988790205 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 = 3.33 ; ; b = 2.4 ; ; c = 1.5 ; ;

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

p = a+b+c = 3.33+2.4+1.5 = 7.23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.23 }{ 2 } = 3.62 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.62 * (3.62-3.33)(3.62-2.4)(3.62-1.5) } ; ; T = sqrt{ 2.64 } = 1.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.63 }{ 3.33 } = 0.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.63 }{ 2.4 } = 1.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.63 }{ 1.5 } = 2.17 ; ;

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{ 3.33**2-2.4**2-1.5**2 }{ 2 * 2.4 * 1.5 } ) = 115° 23'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.4**2-3.33**2-1.5**2 }{ 2 * 3.33 * 1.5 } ) = 40° 36'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.5**2-3.33**2-2.4**2 }{ 2 * 2.4 * 3.33 } ) = 24° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.63 }{ 3.62 } = 0.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.33 }{ 2 * sin 115° 23'59" } = 1.84 ; ;




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