Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 29

Area: T = 55.55657152775
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 13.85549244913° = 13°51'18″ = 0.242181405 rad
Angle ∠ B = β = 15.88329774841° = 15°52'59″ = 0.27772102521 rad
Angle ∠ C = γ = 150.2622098025° = 150°15'44″ = 2.62325683515 rad

Height: ha = 7.93765307539
Height: hb = 6.94444644097
Height: hc = 3.83114286398

Median: ma = 22.34994966386
Median: mb = 21.31990056053
Median: mc = 3.96986269666

Inradius: r = 1.88332445857
Circumradius: R = 29.23219159584

Vertex coordinates: A[29; 0] B[0; 0] C[13.46655172414; 3.83114286398]
Centroid: CG[14.15551724138; 1.27771428799]
Coordinates of the circumscribed circle: U[14.5; -25.38221770263]
Coordinates of the inscribed circle: I[13.5; 1.88332445857]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1455075509° = 166°8'42″ = 0.242181405 rad
∠ B' = β' = 164.1177022516° = 164°7'1″ = 0.27772102521 rad
∠ C' = γ' = 29.73879019754° = 29°44'16″ = 2.62325683515 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 = 14+16+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-14)(29.5-16)(29.5-29) } ; ; T = sqrt{ 3086.44 } = 55.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.56 }{ 14 } = 7.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.56 }{ 16 } = 6.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.56 }{ 29 } = 3.83 ; ;

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{ 16**2+29**2-14**2 }{ 2 * 16 * 29 } ) = 13° 51'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+29**2-16**2 }{ 2 * 14 * 29 } ) = 15° 52'59" ; ;
 gamma = 180° - alpha - beta = 180° - 13° 51'18" - 15° 52'59" = 150° 15'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.56 }{ 29.5 } = 1.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 13° 51'18" } = 29.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 29**2 - 14**2 } }{ 2 } = 22.349 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 14**2 - 16**2 } }{ 2 } = 21.319 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 14**2 - 29**2 } }{ 2 } = 3.969 ; ;
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