Triangle calculator SAS

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


Obtuse isosceles triangle.

Sides: a = 140   b = 140   c = 263.114393382

Area: T = 6299.319857493
Perimeter: p = 543.114393382
Semiperimeter: s = 271.557696691

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 140° = 2.44334609528 rad

Height: ha = 89.99902653561
Height: hb = 89.99902653561
Height: hc = 47.88328200656

Median: ma = 198.7822471775
Median: mb = 198.7822471775
Median: mc = 47.88328200656

Inradius: r = 23.19770427664
Circumradius: R = 204.6666308011

Vertex coordinates: A[263.114393382; 0] B[0; 0] C[131.557696691; 47.88328200656]
Centroid: CG[131.557696691; 15.96109400219]
Coordinates of the circumscribed circle: U[131.557696691; -156.7833487946]
Coordinates of the inscribed circle: I[131.557696691; 23.19770427664]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 40° = 2.44334609528 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 = 140 ; ; b = 140 ; ; gamma = 140° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 140**2+140**2 - 2 * 140 * 140 * cos(140° ) } ; ; c = 263.11 ; ;


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 = 140 ; ; b = 140 ; ; c = 263.11 ; ;

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

p = a+b+c = 140+140+263.11 = 543.11 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 543.11 }{ 2 } = 271.56 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 271.56 * (271.56-140)(271.56-140)(271.56-263.11) } ; ; T = sqrt{ 39681414.51 } = 6299.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6299.32 }{ 140 } = 89.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6299.32 }{ 140 } = 89.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6299.32 }{ 263.11 } = 47.88 ; ;

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{ 140**2-140**2-263.11**2 }{ 2 * 140 * 263.11 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 140**2-140**2-263.11**2 }{ 2 * 140 * 263.11 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 263.11**2-140**2-140**2 }{ 2 * 140 * 140 } ) = 140° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6299.32 }{ 271.56 } = 23.2 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 140 }{ 2 * sin 20° } = 204.67 ; ;




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