Triangle calculator SAS

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


Acute isosceles triangle.

Sides: a = 910   b = 910   c = 142.7965554225

Area: T = 64771.69902499
Perimeter: p = 1962.796555422
Semiperimeter: s = 981.3987777112

Angle ∠ A = α = 85.5° = 85°30' = 1.49222565105 rad
Angle ∠ B = β = 85.5° = 85°30' = 1.49222565105 rad
Angle ∠ C = γ = 9° = 0.15770796327 rad

Height: ha = 142.3555363187
Height: hb = 142.3555363187
Height: hc = 907.1954773697

Median: ma = 466.0698970382
Median: mb = 466.0698970382
Median: mc = 907.1954773697

Inradius: r = 65.99994262882
Circumradius: R = 456.407695031

Vertex coordinates: A[142.7965554225; 0] B[0; 0] C[71.39877771123; 907.1954773697]
Centroid: CG[71.39877771123; 302.3988257899]
Coordinates of the circumscribed circle: U[71.39877771123; 450.7887823387]
Coordinates of the inscribed circle: I[71.39877771123; 65.99994262882]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 94.5° = 94°30' = 1.49222565105 rad
∠ B' = β' = 94.5° = 94°30' = 1.49222565105 rad
∠ C' = γ' = 171° = 0.15770796327 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 = 910 ; ; b = 910 ; ; gamma = 9° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 910**2+910**2 - 2 * 910 * 910 * cos(9° ) } ; ; c = 142.8 ; ;


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 = 910 ; ; b = 910 ; ; c = 142.8 ; ;

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

p = a+b+c = 910+910+142.8 = 1962.8 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1962.8 }{ 2 } = 981.4 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 981.4 * (981.4-910)(981.4-910)(981.4-142.8) } ; ; T = sqrt{ 4195371857.83 } = 64771.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64771.69 }{ 910 } = 142.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64771.69 }{ 910 } = 142.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64771.69 }{ 142.8 } = 907.19 ; ;

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{ 910**2-910**2-142.8**2 }{ 2 * 910 * 142.8 } ) = 85° 30' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 910**2-910**2-142.8**2 }{ 2 * 910 * 142.8 } ) = 85° 30' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 142.8**2-910**2-910**2 }{ 2 * 910 * 910 } ) = 9° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64771.69 }{ 981.4 } = 66 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 910 }{ 2 * sin 85° 30' } = 456.41 ; ;

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

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