Triangle calculator SSS - result

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Acute isosceles triangle.

Sides: a = 910   b = 910   c = 142.8

Area: T = 64773.69443507
Perimeter: p = 1962.8
Semiperimeter: s = 981.4

Angle ∠ A = α = 85.54998596089° = 85°29'59″ = 1.49222540602 rad
Angle ∠ B = β = 85.54998596089° = 85°29'59″ = 1.49222540602 rad
Angle ∠ C = γ = 99.0002807823° = 9°1″ = 0.15770845333 rad

Height: ha = 142.3659767804
Height: hb = 142.3659767804
Height: hc = 907.1954598749

Median: ma = 466.0769651447
Median: mb = 466.0769651447
Median: mc = 907.1954598749

Inradius: r = 66.00113188819
Circumradius: R = 456.4077038325

Vertex coordinates: A[142.8; 0] B[0; 0] C[71.4; 907.1954598749]
Centroid: CG[71.4; 302.3988199583]
Coordinates of the circumscribed circle: U[71.4; 450.7887560424]
Coordinates of the inscribed circle: I[71.4; 66.00113188819]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 94.55001403911° = 94°30'1″ = 1.49222540602 rad
∠ B' = β' = 94.55001403911° = 94°30'1″ = 1.49222540602 rad
∠ C' = γ' = 1710.999719218° = 170°59'59″ = 0.15770845333 rad

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How did we calculate this triangle?

a = 910 ; ; b = 910 ; ; c = 142.8 ; ;

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

p = a+b+c = 910+910+142.8 = 1962.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1962.8 }{ 2 } = 981.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 981.4 * (981.4-910)(981.4-910)(981.4-142.8) } ; ; T = sqrt{ 4195631479.84 } = 64773.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64773.69 }{ 910 } = 142.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64773.69 }{ 910 } = 142.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64773.69 }{ 142.8 } = 907.19 ; ;

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{ 910**2+142.8**2-910**2 }{ 2 * 910 * 142.8 } ) = 85° 29'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 910**2+142.8**2-910**2 }{ 2 * 910 * 142.8 } ) = 85° 29'59" ; ; gamma = 180° - alpha - beta = 180° - 85° 29'59" - 85° 29'59" = 9° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64773.69 }{ 981.4 } = 66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 910 }{ 2 * sin 85° 29'59" } = 456.41 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 910**2+2 * 142.8**2 - 910**2 } }{ 2 } = 466.07 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 142.8**2+2 * 910**2 - 910**2 } }{ 2 } = 466.07 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 910**2+2 * 910**2 - 142.8**2 } }{ 2 } = 907.195 ; ;
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