Triangle calculator SAS

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


Obtuse isosceles triangle.

Sides: a = 89   b = 89   c = 154.1532521874

Area: T = 3429.894361169
Perimeter: p = 332.1532521874
Semiperimeter: s = 166.0766260937

Angle ∠ A = α = 30° = 0.52435987756 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 77.07662609368
Height: hb = 77.07662609368
Height: hc = 44.5

Median: ma = 117.7365933342
Median: mb = 117.7365933342
Median: mc = 44.5

Inradius: r = 20.65325218736
Circumradius: R = 89

Vertex coordinates: A[154.1532521874; 0] B[0; 0] C[77.07662609368; 44.5]
Centroid: CG[77.07662609368; 14.83333333333]
Coordinates of the circumscribed circle: U[77.07662609368; -44.5]
Coordinates of the inscribed circle: I[77.07662609368; 20.65325218736]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150° = 0.52435987756 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 60° = 2.09443951024 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 = 89 ; ; b = 89 ; ; gamma = 120° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 89**2+89**2 - 2 * 89 * 89 * cos(120° ) } ; ; c = 154.15 ; ;


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 = 89 ; ; b = 89 ; ; c = 154.15 ; ;

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

p = a+b+c = 89+89+154.15 = 332.15 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 332.15 }{ 2 } = 166.08 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 166.08 * (166.08-89)(166.08-89)(166.08-154.15) } ; ; T = sqrt{ 11764170.19 } = 3429.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3429.89 }{ 89 } = 77.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3429.89 }{ 89 } = 77.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3429.89 }{ 154.15 } = 44.5 ; ;

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{ 89**2-89**2-154.15**2 }{ 2 * 89 * 154.15 } ) = 30° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 89**2-89**2-154.15**2 }{ 2 * 89 * 154.15 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 154.15**2-89**2-89**2 }{ 2 * 89 * 89 } ) = 120° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3429.89 }{ 166.08 } = 20.65 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 89 }{ 2 * sin 30° } = 89 ; ;




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

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