Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 9.49   b = 6.71   c = 6.71

Area: T = 22.51220498034
Perimeter: p = 22.91
Semiperimeter: s = 11.455

Angle ∠ A = α = 90.00875717202° = 90°27″ = 1.57109284782 rad
Angle ∠ B = β = 44.99662141399° = 44°59'46″ = 0.78553320877 rad
Angle ∠ C = γ = 44.99662141399° = 44°59'46″ = 0.78553320877 rad

Height: ha = 4.74443729828
Height: hb = 6.71099999414
Height: hc = 6.71099999414

Median: ma = 4.74443729828
Median: mb = 7.50224046145
Median: mc = 7.50224046145

Inradius: r = 1.96552596948
Circumradius: R = 4.74550000414

Vertex coordinates: A[6.71; 0] B[0; 0] C[6.71108867362; 6.71099999414]
Centroid: CG[4.47436289121; 2.23766666471]
Coordinates of the circumscribed circle: U[3.355; 3.35554433974]
Coordinates of the inscribed circle: I[4.745; 1.96552596948]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99224282798° = 89°59'33″ = 1.57109284782 rad
∠ B' = β' = 135.004378586° = 135°14″ = 0.78553320877 rad
∠ C' = γ' = 135.004378586° = 135°14″ = 0.78553320877 rad

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How did we calculate this triangle?

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

p = a+b+c = 9.49+6.71+6.71 = 22.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.91 }{ 2 } = 11.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.46 * (11.46-9.49)(11.46-6.71)(11.46-6.71) } ; ; T = sqrt{ 506.79 } = 22.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.51 }{ 9.49 } = 4.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.51 }{ 6.71 } = 6.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.51 }{ 6.71 } = 6.71 ; ;

5. 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{ 6.71**2+6.71**2-9.49**2 }{ 2 * 6.71 * 6.71 } ) = 90° 27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.49**2+6.71**2-6.71**2 }{ 2 * 9.49 * 6.71 } ) = 44° 59'46" ; ;
 gamma = 180° - alpha - beta = 180° - 90° 27" - 44° 59'46" = 44° 59'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.51 }{ 11.46 } = 1.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.49 }{ 2 * sin 90° 27" } = 4.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 6.71**2 - 9.49**2 } }{ 2 } = 4.744 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 9.49**2 - 6.71**2 } }{ 2 } = 7.502 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 9.49**2 - 6.71**2 } }{ 2 } = 7.502 ; ;
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