Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 1.5   b = 1.5   c = 2.12

Area: T = 1.12549991289
Perimeter: p = 5.12
Semiperimeter: s = 2.56

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 = 1.54999988385
Height: hb = 1.54999988385
Height: hc = 1.06113199329

Median: ma = 1.67662159765
Median: mb = 1.67662159765
Median: mc = 1.06113199329

Inradius: r = 0.43994527847
Circumradius: R = 1.06600008208

Vertex coordinates: A[2.12; 0] B[0; 0] C[1.06; 1.06113199329]
Centroid: CG[1.06; 0.3543773311]
Coordinates of the circumscribed circle: U[1.06; 0.00113191121]
Coordinates of the inscribed circle: I[1.06; 0.43994527847]

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 = 1.5+1.5+2.12 = 5.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.12 }{ 2 } = 2.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.56 * (2.56-1.5)(2.56-1.5)(2.56-2.12) } ; ; T = sqrt{ 1.27 } = 1.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.12 }{ 1.5 } = 1.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.12 }{ 1.5 } = 1.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.12 }{ 2.12 } = 1.06 ; ;

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{ 1.5**2+2.12**2-1.5**2 }{ 2 * 1.5 * 2.12 } ) = 45° 2'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.5**2+2.12**2-1.5**2 }{ 2 * 1.5 * 2.12 } ) = 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{ 1.12 }{ 2.56 } = 0.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.5 }{ 2 * sin 45° 2'8" } = 1.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.5**2+2 * 2.12**2 - 1.5**2 } }{ 2 } = 1.676 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.12**2+2 * 1.5**2 - 1.5**2 } }{ 2 } = 1.676 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.5**2+2 * 1.5**2 - 2.12**2 } }{ 2 } = 1.061 ; ;
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