Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 1.05   b = 2.4   c = 1.5

Area: T = 0.50878412492
Perimeter: p = 4.95
Semiperimeter: s = 2.475

Angle ∠ A = α = 16.38876115035° = 16°23'15″ = 0.28660177773 rad
Angle ∠ B = β = 139.8433487791° = 139°50'37″ = 2.44107292994 rad
Angle ∠ C = γ = 23.76989007051° = 23°46'8″ = 0.41548455769 rad

Height: ha = 0.96773166651
Height: hb = 0.4233201041
Height: hc = 0.67771216656

Median: ma = 1.93111589784
Median: mb = 0.48660555524
Median: mc = 1.69437384686

Inradius: r = 0.20551883835
Circumradius: R = 1.8610817729

Vertex coordinates: A[1.5; 0] B[0; 0] C[-0.80325; 0.67771216656]
Centroid: CG[0.23325; 0.22657072219]
Coordinates of the circumscribed circle: U[0.75; 1.70329805109]
Coordinates of the inscribed circle: I[0.075; 0.20551883835]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.6122388497° = 163°36'45″ = 0.28660177773 rad
∠ B' = β' = 40.15765122086° = 40°9'23″ = 2.44107292994 rad
∠ C' = γ' = 156.2311099295° = 156°13'52″ = 0.41548455769 rad

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How did we calculate this triangle?

a = 1.05 ; ; b = 2.4 ; ; c = 1.5 ; ;

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

p = a+b+c = 1.05+2.4+1.5 = 4.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4.95 }{ 2 } = 2.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.48 * (2.48-1.05)(2.48-2.4)(2.48-1.5) } ; ; T = sqrt{ 0.26 } = 0.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.51 }{ 1.05 } = 0.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.51 }{ 2.4 } = 0.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.51 }{ 1.5 } = 0.68 ; ;

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{ 2.4**2+1.5**2-1.05**2 }{ 2 * 2.4 * 1.5 } ) = 16° 23'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.05**2+1.5**2-2.4**2 }{ 2 * 1.05 * 1.5 } ) = 139° 50'37" ; ; gamma = 180° - alpha - beta = 180° - 16° 23'15" - 139° 50'37" = 23° 46'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.51 }{ 2.48 } = 0.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.05 }{ 2 * sin 16° 23'15" } = 1.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.4**2+2 * 1.5**2 - 1.05**2 } }{ 2 } = 1.931 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.5**2+2 * 1.05**2 - 2.4**2 } }{ 2 } = 0.486 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.4**2+2 * 1.05**2 - 1.5**2 } }{ 2 } = 1.694 ; ;
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