Triangle calculator - result

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

You have entered side b, c and area T.

Triangle has two solutions: a=5.76999996488; b=4; c=2 and a=2.74404386516; b=4; c=2.

#1 Obtuse scalene triangle.

Sides: a = 5.76999996488   b = 4   c = 2

Area: T = 2.5
Perimeter: p = 11.76999996488
Semiperimeter: s = 5.85499998244

Angle ∠ A = α = 141.3187812547° = 141°19'4″ = 2.46664611207 rad
Angle ∠ B = β = 26.01443677223° = 26°52″ = 0.45440363696 rad
Angle ∠ C = γ = 12.66878197312° = 12°40'4″ = 0.22110951634 rad

Height: ha = 0.87771930365
Height: hb = 1.25
Height: hc = 2.5

Median: ma = 1.37702193258
Median: mb = 3.77442546282
Median: mc = 4.82113066692

Inradius: r = 0.42773504402
Circumradius: R = 4.56599997191

Vertex coordinates: A[2; 0] B[0; 0] C[5.12224989992; 2.5]
Centroid: CG[2.37441663331; 0.83333333333]
Coordinates of the circumscribed circle: U[1; 4.44989995997]
Coordinates of the inscribed circle: I[1.85499998244; 0.42773504402]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 38.68221874535° = 38°40'56″ = 2.46664611207 rad
∠ B' = β' = 153.9865632278° = 153°59'8″ = 0.45440363696 rad
∠ C' = γ' = 167.3322180269° = 167°19'56″ = 0.22110951634 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 = 5.7 ; ; b = 4 ; ; c = 2 ; ;

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

p = a+b+c = 5.7+4+2 = 11.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.7 }{ 2 } = 5.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.85 * (5.85-5.7)(5.85-4)(5.85-2) } ; ; T = sqrt{ 6.25 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 5.7 } = 0.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 4 } = 1.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 2 } = 2.5 ; ;

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{ 5.7**2-4**2-2**2 }{ 2 * 4 * 2 } ) = 141° 19'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-5.7**2-2**2 }{ 2 * 5.7 * 2 } ) = 26° 52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2**2-5.7**2-4**2 }{ 2 * 4 * 5.7 } ) = 12° 40'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 5.85 } = 0.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.7 }{ 2 * sin 141° 19'4" } = 4.56 ; ;





#2 Obtuse scalene triangle.

Sides: a = 2.74404386516   b = 4   c = 2

Area: T = 2.5
Perimeter: p = 8.74404386516
Semiperimeter: s = 4.37702193258

Angle ∠ A = α = 38.68221874535° = 38°40'56″ = 0.67551315329 rad
Angle ∠ B = β = 114.1880061185° = 114°10'48″ = 1.99328180078 rad
Angle ∠ C = γ = 27.13877513611° = 27°8'16″ = 0.47436431128 rad

Height: ha = 1.82545254266
Height: hb = 1.25
Height: hc = 2.5

Median: ma = 2.85499998244
Median: mb = 1.32547648854
Median: mc = 3.27994819715

Inradius: r = 0.57220536691
Circumradius: R = 2.19223509213

Vertex coordinates: A[2; 0] B[0; 0] C[-1.12224989992; 2.5]
Centroid: CG[0.29325003336; 0.83333333333]
Coordinates of the circumscribed circle: U[1; 1.95110004003]
Coordinates of the inscribed circle: I[0.37702193258; 0.57220536691]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3187812547° = 141°19'4″ = 0.67551315329 rad
∠ B' = β' = 65.82199388146° = 65°49'12″ = 1.99328180078 rad
∠ C' = γ' = 152.8622248639° = 152°51'44″ = 0.47436431128 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 = 2.74 ; ; b = 4 ; ; c = 2 ; ;

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

p = a+b+c = 2.74+4+2 = 8.74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.74 }{ 2 } = 4.37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.37 * (4.37-2.74)(4.37-4)(4.37-2) } ; ; T = sqrt{ 6.25 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 2.74 } = 1.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 4 } = 1.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 2 } = 2.5 ; ;

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{ 2.74**2-4**2-2**2 }{ 2 * 4 * 2 } ) = 38° 40'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-2.74**2-2**2 }{ 2 * 2.74 * 2 } ) = 114° 10'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2**2-2.74**2-4**2 }{ 2 * 4 * 2.74 } ) = 27° 8'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 4.37 } = 0.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.74 }{ 2 * sin 38° 40'56" } = 2.19 ; ;




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