Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 7.6   b = 6.7   c = 3.56879990391

Area: T = 11.95327459885
Perimeter: p = 17.86879990391
Semiperimeter: s = 8.93439995196

Angle ∠ A = α = 90.16770333079° = 90°10'1″ = 1.5743711608 rad
Angle ∠ B = β = 61.83329666921° = 61°49'59″ = 1.07991888551 rad
Angle ∠ C = γ = 28° = 0.48986921906 rad

Height: ha = 3.14554594707
Height: hb = 3.56879838772
Height: hc = 6.76999715288

Median: ma = 3.79108189843
Median: mb = 4.90113068228
Median: mc = 6.93884685424

Inradius: r = 1.3387894183
Circumradius: R = 3.88000161479

Vertex coordinates: A[3.56879990391; 0] B[0; 0] C[3.58875313954; 6.76999715288]
Centroid: CG[2.38551768115; 2.23333238429]
Coordinates of the circumscribed circle: U[1.78439995196; 3.35552151106]
Coordinates of the inscribed circle: I[2.23439995196; 1.3387894183]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.83329666921° = 89°49'59″ = 1.5743711608 rad
∠ B' = β' = 118.1677033308° = 118°10'1″ = 1.07991888551 rad
∠ C' = γ' = 152° = 0.48986921906 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 = 7.6 ; ; b = 6.7 ; ; gamma = 28° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 7.6**2+6.7**2 - 2 * 7.6 * 6.7 * cos(28° ) } ; ; c = 3.57 ; ;


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 = 7.6 ; ; b = 6.7 ; ; c = 3.57 ; ;

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

p = a+b+c = 7.6+6.7+3.57 = 17.87 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.87 }{ 2 } = 8.93 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.93 * (8.93-7.6)(8.93-6.7)(8.93-3.57) } ; ; T = sqrt{ 142.87 } = 11.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.95 }{ 7.6 } = 3.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.95 }{ 6.7 } = 3.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.95 }{ 3.57 } = 6.7 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 6.7**2+3.57**2-7.6**2 }{ 2 * 6.7 * 3.57 } ) = 90° 10'1" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.6**2+3.57**2-6.7**2 }{ 2 * 7.6 * 3.57 } ) = 61° 49'59" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 7.6**2+6.7**2-3.57**2 }{ 2 * 7.6 * 6.7 } ) = 28° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.95 }{ 8.93 } = 1.34 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.6 }{ 2 * sin 90° 10'1" } = 3.8 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.7**2+2 * 3.57**2 - 7.6**2 } }{ 2 } = 3.791 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.57**2+2 * 7.6**2 - 6.7**2 } }{ 2 } = 4.901 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.7**2+2 * 7.6**2 - 3.57**2 } }{ 2 } = 6.938 ; ;
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