Triangle calculator SAS

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


Obtuse isosceles triangle.

Sides: a = 9.525   b = 9.525   c = 16.49877839421

Area: T = 39.28553480121
Perimeter: p = 35.54877839421
Semiperimeter: s = 17.7743891971

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

Height: ha = 8.2498891971
Height: hb = 8.2498891971
Height: hc = 4.76325

Median: ma = 12.66003906189
Median: mb = 12.66003906189
Median: mc = 4.76325

Inradius: r = 2.21102839421
Circumradius: R = 9.525

Vertex coordinates: A[16.49877839421; 0] B[0; 0] C[8.2498891971; 4.76325]
Centroid: CG[8.2498891971; 1.58875]
Coordinates of the circumscribed circle: U[8.2498891971; -4.76325]
Coordinates of the inscribed circle: I[8.2498891971; 2.21102839421]

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

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How did we calculate this triangle?

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

a = 9.53 ; ; b = 9.53 ; ; gamma = 120° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 9.53**2+9.53**2 - 2 * 9.53 * 9.53 * cos(120° ) } ; ; c = 16.5 ; ;


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 = 9.53 ; ; b = 9.53 ; ; c = 16.5 ; ;

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

p = a+b+c = 9.53+9.53+16.5 = 35.55 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.55 }{ 2 } = 17.77 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.77 * (17.77-9.53)(17.77-9.53)(17.77-16.5) } ; ; T = sqrt{ 1543.34 } = 39.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.29 }{ 9.53 } = 8.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.29 }{ 9.53 } = 8.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.29 }{ 16.5 } = 4.76 ; ;

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{ 9.53**2-9.53**2-16.5**2 }{ 2 * 9.53 * 16.5 } ) = 30° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.53**2-9.53**2-16.5**2 }{ 2 * 9.53 * 16.5 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16.5**2-9.53**2-9.53**2 }{ 2 * 9.53 * 9.53 } ) = 120° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.29 }{ 17.77 } = 2.21 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.53 }{ 2 * sin 30° } = 9.53 ; ;




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