Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 0.75   b = 0.75   c = 1.06

Area: T = 0.28112497822
Perimeter: p = 2.56
Semiperimeter: s = 1.28

Angle ∠ A = α = 45.03656507165° = 45°2'8″ = 0.78660203858 rad
Angle ∠ B = β = 45.03656507165° = 45°2'8″ = 0.78660203858 rad
Angle ∠ C = γ = 89.92986985671° = 89°55'43″ = 1.5769551882 rad

Height: ha = 0.75499994193
Height: hb = 0.75499994193
Height: hc = 0.53106599665

Median: ma = 0.83881079883
Median: mb = 0.83881079883
Median: mc = 0.53106599665

Inradius: r = 0.22197263924
Circumradius: R = 0.53300004104

Vertex coordinates: A[1.06; 0] B[0; 0] C[0.53; 0.53106599665]
Centroid: CG[0.53; 0.17768866555]
Coordinates of the circumscribed circle: U[0.53; 0.00106595561]
Coordinates of the inscribed circle: I[0.53; 0.22197263924]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9644349284° = 134°57'52″ = 0.78660203858 rad
∠ B' = β' = 134.9644349284° = 134°57'52″ = 0.78660203858 rad
∠ C' = γ' = 90.07113014329° = 90°4'17″ = 1.5769551882 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 = 0.75+0.75+1.06 = 2.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2.56 }{ 2 } = 1.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.28 * (1.28-0.75)(1.28-0.75)(1.28-1.06) } ; ; T = sqrt{ 0.08 } = 0.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.28 }{ 0.75 } = 0.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.28 }{ 0.75 } = 0.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.28 }{ 1.06 } = 0.53 ; ;

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{ 0.75**2+1.06**2-0.75**2 }{ 2 * 0.75 * 1.06 } ) = 45° 2'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.75**2+1.06**2-0.75**2 }{ 2 * 0.75 * 1.06 } ) = 45° 2'8" ; ; gamma = 180° - alpha - beta = 180° - 45° 2'8" - 45° 2'8" = 89° 55'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.28 }{ 1.28 } = 0.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.75 }{ 2 * sin 45° 2'8" } = 0.53 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.75**2+2 * 1.06**2 - 0.75**2 } }{ 2 } = 0.838 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.06**2+2 * 0.75**2 - 0.75**2 } }{ 2 } = 0.838 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.75**2+2 * 0.75**2 - 1.06**2 } }{ 2 } = 0.531 ; ;
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