Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 0.6   b = 2.33   c = 2.25

Area: T = 0.67549981037
Perimeter: p = 5.18
Semiperimeter: s = 2.59

Angle ∠ A = α = 14.92223658655° = 14°55'21″ = 0.26604444165 rad
Angle ∠ B = β = 90.13658123453° = 90°8'9″ = 1.57331666994 rad
Angle ∠ C = γ = 74.94218217892° = 74°56'31″ = 1.30879815377 rad

Height: ha = 2.2549993679
Height: hb = 0.57993975139
Height: hc = 0.65999983144

Median: ma = 2.27106166563
Median: mb = 1.1643625799
Median: mc = 1.2766254285

Inradius: r = 0.26106170285
Circumradius: R = 1.16550032729

Vertex coordinates: A[2.25; 0] B[0; 0] C[-0.00114222222; 0.65999983144]
Centroid: CG[0.75495259259; 0.21999994381]
Coordinates of the circumscribed circle: U[1.125; 0.3032667517]
Coordinates of the inscribed circle: I[0.26; 0.26106170285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.0787634135° = 165°4'39″ = 0.26604444165 rad
∠ B' = β' = 89.86441876547° = 89°51'51″ = 1.57331666994 rad
∠ C' = γ' = 105.0588178211° = 105°3'29″ = 1.30879815377 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 = 0.6+2.33+2.25 = 5.18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.18 }{ 2 } = 2.59 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.59 * (2.59-0.6)(2.59-2.33)(2.59-2.25) } ; ; T = sqrt{ 0.46 } = 0.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.67 }{ 0.6 } = 2.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.67 }{ 2.33 } = 0.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.67 }{ 2.25 } = 0.6 ; ;

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{ 2.33**2+2.25**2-0.6**2 }{ 2 * 2.33 * 2.25 } ) = 14° 55'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.6**2+2.25**2-2.33**2 }{ 2 * 0.6 * 2.25 } ) = 90° 8'9" ; ; gamma = 180° - alpha - beta = 180° - 14° 55'21" - 90° 8'9" = 74° 56'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.67 }{ 2.59 } = 0.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.6 }{ 2 * sin 14° 55'21" } = 1.17 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.33**2+2 * 2.25**2 - 0.6**2 } }{ 2 } = 2.271 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.25**2+2 * 0.6**2 - 2.33**2 } }{ 2 } = 1.164 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.33**2+2 * 0.6**2 - 2.25**2 } }{ 2 } = 1.276 ; ;
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