Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 10.2   b = 14.42   c = 10.2

Area: T = 52.02199876124
Perimeter: p = 34.82
Semiperimeter: s = 17.41

Angle ∠ A = α = 45.02197704599° = 45°1'11″ = 0.7865743223 rad
Angle ∠ B = β = 89.96604590802° = 89°57'38″ = 1.57701062076 rad
Angle ∠ C = γ = 45.02197704599° = 45°1'11″ = 0.7865743223 rad

Height: ha = 10.21999975711
Height: hb = 7.21549774774
Height: hc = 10.21999975711

Median: ma = 11.40107982177
Median: mb = 7.21549774774
Median: mc = 11.40107982177

Inradius: r = 2.98879372552
Circumradius: R = 7.21100017169

Vertex coordinates: A[10.2; 0] B[0; 0] C[0.00770392157; 10.21999975711]
Centroid: CG[3.40223464052; 3.43999991904]
Coordinates of the circumscribed circle: U[5.1; 5.09664816058]
Coordinates of the inscribed circle: I[2.99; 2.98879372552]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.988022954° = 134°58'49″ = 0.7865743223 rad
∠ B' = β' = 90.04395409198° = 90°2'22″ = 1.57701062076 rad
∠ C' = γ' = 134.988022954° = 134°58'49″ = 0.7865743223 rad

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How did we calculate this triangle?

a = 10.2 ; ; b = 14.42 ; ; c = 10.2 ; ;

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

p = a+b+c = 10.2+14.42+10.2 = 34.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34.82 }{ 2 } = 17.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.41 * (17.41-10.2)(17.41-14.42)(17.41-10.2) } ; ; T = sqrt{ 2706.08 } = 52.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.02 }{ 10.2 } = 10.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.02 }{ 14.42 } = 7.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.02 }{ 10.2 } = 10.2 ; ;

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{ 14.42**2+10.2**2-10.2**2 }{ 2 * 14.42 * 10.2 } ) = 45° 1'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.2**2+10.2**2-14.42**2 }{ 2 * 10.2 * 10.2 } ) = 89° 57'38" ; ; gamma = 180° - alpha - beta = 180° - 45° 1'11" - 89° 57'38" = 45° 1'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.02 }{ 17.41 } = 2.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.2 }{ 2 * sin 45° 1'11" } = 7.21 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.42**2+2 * 10.2**2 - 10.2**2 } }{ 2 } = 11.401 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.2**2+2 * 10.2**2 - 14.42**2 } }{ 2 } = 7.215 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.42**2+2 * 10.2**2 - 10.2**2 } }{ 2 } = 11.401 ; ;
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