Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Acute isosceles triangle.

Sides: a = 72   b = 72   c = 60.85770296907

Area: T = 1985.587719656
Perimeter: p = 204.8577029691
Semiperimeter: s = 102.4298514845

Angle ∠ A = α = 65° = 1.13444640138 rad
Angle ∠ B = β = 65° = 1.13444640138 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 55.15551999046
Height: hb = 55.15551999046
Height: hc = 65.25441606666

Median: ma = 56.10551604702
Median: mb = 56.10551604702
Median: mc = 65.25441606666

Inradius: r = 19.38551018885
Circumradius: R = 39.72216050826

Vertex coordinates: A[60.85770296907; 0] B[0; 0] C[30.42985148453; 65.25441606666]
Centroid: CG[30.42985148453; 21.75113868889]
Coordinates of the circumscribed circle: U[30.42985148453; 25.5332555584]
Coordinates of the inscribed circle: I[30.42985148453; 19.38551018885]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115° = 1.13444640138 rad
∠ B' = β' = 115° = 1.13444640138 rad
∠ C' = γ' = 130° = 0.8732664626 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 72 ; ; b = 72 ; ; gamma = 50° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 72**2+72**2 - 2 * 72 * 72 * cos(50° ) } ; ; c = 60.86 ; ;


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 = 72 ; ; b = 72 ; ; c = 60.86 ; ;

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

p = a+b+c = 72+72+60.86 = 204.86 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 204.86 }{ 2 } = 102.43 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 102.43 * (102.43-72)(102.43-72)(102.43-60.86) } ; ; T = sqrt{ 3942556.52 } = 1985.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1985.59 }{ 72 } = 55.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1985.59 }{ 72 } = 55.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1985.59 }{ 60.86 } = 65.25 ; ;

6. 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{ 72**2-72**2-60.86**2 }{ 2 * 72 * 60.86 } ) = 65° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 72**2-72**2-60.86**2 }{ 2 * 72 * 60.86 } ) = 65° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60.86**2-72**2-72**2 }{ 2 * 72 * 72 } ) = 50° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1985.59 }{ 102.43 } = 19.39 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 72 }{ 2 * sin 65° } = 39.72 ; ;




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

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