Triangle calculator SAS

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


Acute scalene triangle.

Sides: a = 64.68875   b = 64.875   c = 25.27770588054

Area: T = 802.9854945103
Perimeter: p = 154.8439558805
Semiperimeter: s = 77.42197794027

Angle ∠ A = α = 78.3333154482° = 78°19'59″ = 1.36771714592 rad
Angle ∠ B = β = 79.1676845518° = 79°10'1″ = 1.38217221127 rad
Angle ∠ C = γ = 22.5° = 22°30' = 0.39326990817 rad

Height: ha = 24.82765876747
Height: hb = 24.75548345311
Height: hc = 63.53546818856

Median: ma = 37.11877787504
Median: mb = 36.87215306544
Median: mc = 63.53664990786

Inradius: r = 10.37218319956
Circumradius: R = 33.02660688962

Vertex coordinates: A[25.27770588054; 0] B[0; 0] C[12.1587995474; 63.53546818856]
Centroid: CG[12.47883514265; 21.17882272952]
Coordinates of the circumscribed circle: U[12.63985294027; 30.51221090925]
Coordinates of the inscribed circle: I[12.54547794027; 10.37218319956]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.6676845518° = 101°40'1″ = 1.36771714592 rad
∠ B' = β' = 100.8333154482° = 100°49'59″ = 1.38217221127 rad
∠ C' = γ' = 157.5° = 157°30' = 0.39326990817 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 = 64.69 ; ; b = 64.88 ; ; gamma = 22° 30' ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 64.69**2+64.88**2 - 2 * 64.69 * 64.88 * cos(22° 30') } ; ; c = 25.28 ; ;


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 = 64.69 ; ; b = 64.88 ; ; c = 25.28 ; ;

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

p = a+b+c = 64.69+64.88+25.28 = 154.84 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 154.84 }{ 2 } = 77.42 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 77.42 * (77.42-64.69)(77.42-64.88)(77.42-25.28) } ; ; T = sqrt{ 644784.82 } = 802.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 802.98 }{ 64.69 } = 24.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 802.98 }{ 64.88 } = 24.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 802.98 }{ 25.28 } = 63.53 ; ;

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{ 64.69**2-64.88**2-25.28**2 }{ 2 * 64.88 * 25.28 } ) = 78° 19'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 64.88**2-64.69**2-25.28**2 }{ 2 * 64.69 * 25.28 } ) = 79° 10'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25.28**2-64.69**2-64.88**2 }{ 2 * 64.88 * 64.69 } ) = 22° 30' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 802.98 }{ 77.42 } = 10.37 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 64.69 }{ 2 * sin 78° 19'59" } = 33.03 ; ;




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