Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 71.8   b = 46.15   c = 55

Area: T = 1269.125499571
Perimeter: p = 172.95
Semiperimeter: s = 86.475

Angle ∠ A = α = 90.00547121024° = 90°17″ = 1.57108785685 rad
Angle ∠ B = β = 39.998775982° = 39°59'52″ = 0.69880926023 rad
Angle ∠ C = γ = 49.99875280776° = 49°59'51″ = 0.87326214828 rad

Height: ha = 35.35216711896
Height: hb = 554.999999814
Height: hc = 46.15499998439

Median: ma = 35.89770925006
Median: mb = 59.64661597674
Median: mc = 53.72441216773

Inradius: r = 14.67662069466
Circumradius: R = 35.99000001214

Vertex coordinates: A[55; 0] B[0; 0] C[55.00437954545; 46.15499998439]
Centroid: CG[36.66879318182; 15.38333332813]
Coordinates of the circumscribed circle: U[27.5; 23.07772617248]
Coordinates of the inscribed circle: I[40.325; 14.67662069466]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99552878976° = 89°59'43″ = 1.57108785685 rad
∠ B' = β' = 140.002224018° = 140°8″ = 0.69880926023 rad
∠ C' = γ' = 130.0022471922° = 130°9″ = 0.87326214828 rad

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How did we calculate this triangle?

a = 71.8 ; ; b = 46.15 ; ; c = 55 ; ;

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

p = a+b+c = 71.8+46.15+55 = 172.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 172.95 }{ 2 } = 86.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 86.48 * (86.48-71.8)(86.48-46.15)(86.48-55) } ; ; T = sqrt{ 1610678.25 } = 1269.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1269.12 }{ 71.8 } = 35.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1269.12 }{ 46.15 } = 55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1269.12 }{ 55 } = 46.15 ; ;

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{ 46.15**2+55**2-71.8**2 }{ 2 * 46.15 * 55 } ) = 90° 17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 71.8**2+55**2-46.15**2 }{ 2 * 71.8 * 55 } ) = 39° 59'52" ; ; gamma = 180° - alpha - beta = 180° - 90° 17" - 39° 59'52" = 49° 59'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1269.12 }{ 86.48 } = 14.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 71.8 }{ 2 * sin 90° 17" } = 35.9 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 46.15**2+2 * 55**2 - 71.8**2 } }{ 2 } = 35.897 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 71.8**2 - 46.15**2 } }{ 2 } = 59.646 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 46.15**2+2 * 71.8**2 - 55**2 } }{ 2 } = 53.724 ; ;
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