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=113.194354285; b=265; c=172 and a=359.043991497; b=265; c=172.

#1 Obtuse scalene triangle.

Sides: a = 113.194354285   b = 265   c = 172

Area: T = 6809.015508386
Perimeter: p = 550.194354285
Semiperimeter: s = 275.0976771425

Angle ∠ A = α = 17.38438646978° = 17°23'2″ = 0.30334056757 rad
Angle ∠ B = β = 135.6166135302° = 135°36'58″ = 2.36769480799 rad
Angle ∠ C = γ = 27° = 0.4711238898 rad

Height: ha = 120.3077482431
Height: hb = 51.38987930858
Height: hc = 79.17545939984

Median: ma = 216.1054848313
Median: mb = 60.35501372945
Median: mc = 184.7243818365

Inradius: r = 24.75113449489
Circumradius: R = 189.4311276754

Vertex coordinates: A[172; 0] B[0; 0] C[-80.89659937705; 79.17545939984]
Centroid: CG[30.36880020765; 26.39215313328]
Coordinates of the circumscribed circle: U[86; 168.7854503473]
Coordinates of the inscribed circle: I[10.0976771425; 24.75113449489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6166135302° = 162°36'58″ = 0.30334056757 rad
∠ B' = β' = 44.38438646978° = 44°23'2″ = 2.36769480799 rad
∠ C' = γ' = 153° = 0.4711238898 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 = 113.19 ; ; b = 265 ; ; c = 172 ; ;

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

p = a+b+c = 113.19+265+172 = 550.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 550.19 }{ 2 } = 275.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 275.1 * (275.1-113.19)(275.1-265)(275.1-172) } ; ; T = sqrt{ 46362686.41 } = 6809.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6809.02 }{ 113.19 } = 120.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6809.02 }{ 265 } = 51.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6809.02 }{ 172 } = 79.17 ; ;

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{ 113.19**2-265**2-172**2 }{ 2 * 265 * 172 } ) = 17° 23'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 265**2-113.19**2-172**2 }{ 2 * 113.19 * 172 } ) = 135° 36'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 172**2-113.19**2-265**2 }{ 2 * 265 * 113.19 } ) = 27° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6809.02 }{ 275.1 } = 24.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 113.19 }{ 2 * sin 17° 23'2" } = 189.43 ; ;





#2 Obtuse scalene triangle.

Sides: a = 359.043991497   b = 265   c = 172

Area: T = 21597.59441311
Perimeter: p = 796.043991497
Semiperimeter: s = 398.0219957485

Angle ∠ A = α = 108.6166135302° = 108°36'58″ = 1.89657091818 rad
Angle ∠ B = β = 44.38438646978° = 44°23'2″ = 0.77546445737 rad
Angle ∠ C = γ = 27° = 0.4711238898 rad

Height: ha = 120.3077482431
Height: hb = 163.0010710424
Height: hc = 251.1354815478

Median: ma = 132.9555198712
Median: mb = 248.3765885043
Median: mc = 303.5977315981

Inradius: r = 54.26325909203
Circumradius: R = 189.4311276754

Vertex coordinates: A[172; 0] B[0; 0] C[256.5954943435; 251.1354815478]
Centroid: CG[142.8654981145; 83.71216051594]
Coordinates of the circumscribed circle: U[86; 168.7854503473]
Coordinates of the inscribed circle: I[133.0219957485; 54.26325909203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 71.38438646978° = 71°23'2″ = 1.89657091818 rad
∠ B' = β' = 135.6166135302° = 135°36'58″ = 0.77546445737 rad
∠ C' = γ' = 153° = 0.4711238898 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 = 359.04 ; ; b = 265 ; ; c = 172 ; ;

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

p = a+b+c = 359.04+265+172 = 796.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 796.04 }{ 2 } = 398.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 398.02 * (398.02-359.04)(398.02-265)(398.02-172) } ; ; T = sqrt{ 466456072.25 } = 21597.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21597.59 }{ 359.04 } = 120.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21597.59 }{ 265 } = 163 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21597.59 }{ 172 } = 251.13 ; ;

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{ 359.04**2-265**2-172**2 }{ 2 * 265 * 172 } ) = 108° 36'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 265**2-359.04**2-172**2 }{ 2 * 359.04 * 172 } ) = 44° 23'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 172**2-359.04**2-265**2 }{ 2 * 265 * 359.04 } ) = 27° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21597.59 }{ 398.02 } = 54.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 359.04 }{ 2 * sin 108° 36'58" } = 189.43 ; ;




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