Triangle calculator SAS

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


Acute isosceles triangle.

Sides: a = 3.7   b = 3.7   c = 4.2444465629

Area: T = 6.43221959893
Perimeter: p = 11.6444465629
Semiperimeter: s = 5.82222328145

Angle ∠ A = α = 55° = 0.96599310886 rad
Angle ∠ B = β = 55° = 0.96599310886 rad
Angle ∠ C = γ = 70° = 1.22217304764 rad

Height: ha = 3.47768626969
Height: hb = 3.47768626969
Height: hc = 3.03108625639

Median: ma = 3.52656551502
Median: mb = 3.52656551502
Median: mc = 3.03108625639

Inradius: r = 1.10547644768
Circumradius: R = 2.25884329892

Vertex coordinates: A[4.2444465629; 0] B[0; 0] C[2.12222328145; 3.03108625639]
Centroid: CG[2.12222328145; 1.01102875213]
Coordinates of the circumscribed circle: U[2.12222328145; 0.77224295747]
Coordinates of the inscribed circle: I[2.12222328145; 1.10547644768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125° = 0.96599310886 rad
∠ B' = β' = 125° = 0.96599310886 rad
∠ C' = γ' = 110° = 1.22217304764 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 = 3.7 ; ; b = 3.7 ; ; gamma = 70° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 3.7**2+3.7**2 - 2 * 3.7 * 3.7 * cos(70° ) } ; ; c = 4.24 ; ;


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 = 3.7 ; ; b = 3.7 ; ; c = 4.24 ; ;

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

p = a+b+c = 3.7+3.7+4.24 = 11.64 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.64 }{ 2 } = 5.82 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.82 * (5.82-3.7)(5.82-3.7)(5.82-4.24) } ; ; T = sqrt{ 41.37 } = 6.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.43 }{ 3.7 } = 3.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.43 }{ 3.7 } = 3.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.43 }{ 4.24 } = 3.03 ; ;

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{ 3.7**2-3.7**2-4.24**2 }{ 2 * 3.7 * 4.24 } ) = 55° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.7**2-3.7**2-4.24**2 }{ 2 * 3.7 * 4.24 } ) = 55° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.24**2-3.7**2-3.7**2 }{ 2 * 3.7 * 3.7 } ) = 70° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.43 }{ 5.82 } = 1.1 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.7 }{ 2 * sin 55° } = 2.26 ; ;




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

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