Triangle calculator

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

You have entered side a, c and height hc.

Triangle has two solutions: a=7.42; b=19.17114422912; c=12.5 and a=7.42; b=7.4210822089; c=12.5.

#1 Obtuse scalene triangle.

Sides: a = 7.42   b = 19.17114422912   c = 12.5

Area: T = 25
Perimeter: p = 39.09114422912
Semiperimeter: s = 19.54657211456

Angle ∠ A = α = 12.04328794408° = 12°2'34″ = 0.21101878977 rad
Angle ∠ B = β = 147.3798725566° = 147°22'43″ = 2.57222440085 rad
Angle ∠ C = γ = 20.57883949933° = 20°34'42″ = 0.35991607474 rad

Height: ha = 6.73985444744
Height: hb = 2.60880458236
Height: hc = 4

Median: ma = 15.75222379287
Median: mb = 3.71104110445
Median: mc = 13.12439399481

Inradius: r = 1.27990523212
Circumradius: R = 17.78215127251

Vertex coordinates: A[12.5; 0] B[0; 0] C[-6.25495119809; 4]
Centroid: CG[2.08334960064; 1.33333333333]
Coordinates of the circumscribed circle: U[6.25; 16.64769124702]
Coordinates of the inscribed circle: I[0.37442788544; 1.27990523212]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9577120559° = 167°57'26″ = 0.21101878977 rad
∠ B' = β' = 32.62112744342° = 32°37'17″ = 2.57222440085 rad
∠ C' = γ' = 159.4221605007° = 159°25'18″ = 0.35991607474 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 = 7.42 ; ; b = 19.17 ; ; c = 12.5 ; ;

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

p = a+b+c = 7.42+19.17+12.5 = 39.09 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39.09 }{ 2 } = 19.55 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.55 * (19.55-7.42)(19.55-19.17)(19.55-12.5) } ; ; T = sqrt{ 625 } = 25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25 }{ 7.42 } = 6.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25 }{ 19.17 } = 2.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25 }{ 12.5 } = 4 ; ;

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{ 7.42**2-19.17**2-12.5**2 }{ 2 * 19.17 * 12.5 } ) = 12° 2'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19.17**2-7.42**2-12.5**2 }{ 2 * 7.42 * 12.5 } ) = 147° 22'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.5**2-7.42**2-19.17**2 }{ 2 * 19.17 * 7.42 } ) = 20° 34'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25 }{ 19.55 } = 1.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.42 }{ 2 * sin 12° 2'34" } = 17.78 ; ;





#2 Obtuse scalene triangle.

Sides: a = 7.42   b = 7.4210822089   c = 12.5

Area: T = 25
Perimeter: p = 27.3410822089
Semiperimeter: s = 13.67704110445

Angle ∠ A = α = 32.61772119332° = 32°37'2″ = 0.56992777411 rad
Angle ∠ B = β = 32.62112744342° = 32°37'17″ = 0.56993486451 rad
Angle ∠ C = γ = 114.7621513633° = 114°45'41″ = 2.00329662675 rad

Height: ha = 6.73985444744
Height: hb = 6.73877979691
Height: hc = 4

Median: ma = 9.58661984247
Median: mb = 9.58657211456
Median: mc = 44.0000000298

Inradius: r = 1.82987672491
Circumradius: R = 6.88328124875

Vertex coordinates: A[12.5; 0] B[0; 0] C[6.25495119809; 4]
Centroid: CG[6.2549837327; 1.33333333333]
Coordinates of the circumscribed circle: U[6.25; -2.88328124702]
Coordinates of the inscribed circle: I[6.25495889555; 1.82987672491]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.3832788067° = 147°22'58″ = 0.56992777411 rad
∠ B' = β' = 147.3798725566° = 147°22'43″ = 0.56993486451 rad
∠ C' = γ' = 65.23884863674° = 65°14'19″ = 2.00329662675 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 = 7.42 ; ; b = 7.42 ; ; c = 12.5 ; ;

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

p = a+b+c = 7.42+7.42+12.5 = 27.34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.34 }{ 2 } = 13.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.67 * (13.67-7.42)(13.67-7.42)(13.67-12.5) } ; ; T = sqrt{ 625 } = 25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25 }{ 7.42 } = 6.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25 }{ 7.42 } = 6.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25 }{ 12.5 } = 4 ; ;

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{ 7.42**2-7.42**2-12.5**2 }{ 2 * 7.42 * 12.5 } ) = 32° 37'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.42**2-7.42**2-12.5**2 }{ 2 * 7.42 * 12.5 } ) = 32° 37'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.5**2-7.42**2-7.42**2 }{ 2 * 7.42 * 7.42 } ) = 114° 45'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25 }{ 13.67 } = 1.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.42 }{ 2 * sin 32° 37'2" } = 6.88 ; ;




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