Triangle calculator

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

You have entered side a, b and angle β.

Right scalene triangle.

Sides: a = 307.715   b = 347   c = 160.3766054244

Area: T = 24675.05987659
Perimeter: p = 815.0911054244
Semiperimeter: s = 407.5465527122

Angle ∠ A = α = 62.47222069266° = 62°28'20″ = 1.09903457019 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 27.52877930734° = 27°31'40″ = 0.48804506249 rad

Height: ha = 160.3766054244
Height: hb = 142.2199358881
Height: hc = 307.715

Median: ma = 222.2444480429
Median: mb = 173.5
Median: mc = 317.992157366

Inradius: r = 60.54655271222
Circumradius: R = 173.5

Vertex coordinates: A[160.3766054244; 0] B[0; 0] C[-0; 307.715]
Centroid: CG[53.45986847481; 102.5721666667]
Coordinates of the circumscribed circle: U[80.18880271222; 153.85875]
Coordinates of the inscribed circle: I[60.54655271222; 60.54655271222]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.5287793073° = 117°31'40″ = 1.09903457019 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 152.4722206927° = 152°28'20″ = 0.48804506249 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side a, b and angle β.

a = 307.715 ; ; b = 347 ; ; beta = 90° ; ;

2. From angle β, side a and b we calculate c - by using the law of cosines and quadratic equation:

b**2 = a**2 + c**2 - 2a c cos beta ; ; ; ; 347**2 = 307.715**2 + c**2 - 2 * 307.715 * c * cos(90° ) ; ; ; ; ; ; c**2 -25720.479 =0 ; ; a=1; b=-0; c=-25720.479 ; ; D = b**2 - 4ac = 0**2 - 4 * 1 * (-25720.479) = 102881.9151 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -b ± sqrt{ D } }{ 2a } = fraction{ ± sqrt{ 102881.92 } }{ 2 } ; ; c_{1,2} = ± 160.376054244 ; ; c_{1} = 160.376054244 ; ; c_{2} = -160.376054244 ; ; ; ;
(c -160.376054244) (c +160.376054244) = 0 ; ; ; ; c > 0 ; ; ; ; c = 160.376 ; ;


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 = 307.72 ; ; b = 347 ; ; c = 160.38 ; ;

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

p = a+b+c = 307.72+347+160.38 = 815.09 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 815.09 }{ 2 } = 407.55 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 407.55 * (407.55-307.72)(407.55-347)(407.55-160.38) } ; ; T = sqrt{ 608858525.1 } = 24675.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24675.06 }{ 307.72 } = 160.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24675.06 }{ 347 } = 142.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24675.06 }{ 160.38 } = 307.72 ; ;

7. 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{ 307.72**2-347**2-160.38**2 }{ 2 * 347 * 160.38 } ) = 62° 28'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 347**2-307.72**2-160.38**2 }{ 2 * 307.72 * 160.38 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 160.38**2-307.72**2-347**2 }{ 2 * 347 * 307.72 } ) = 27° 31'40" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24675.06 }{ 407.55 } = 60.55 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 307.72 }{ 2 * sin 62° 28'20" } = 173.5 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.