Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 24

Area: T = 97.58881012214
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 32.83105360991° = 32°49'50″ = 0.57330009501 rad
Angle ∠ B = β = 35.51325704274° = 35°30'45″ = 0.62198112798 rad
Angle ∠ C = γ = 111.6576893474° = 111°39'25″ = 1.94987804237 rad

Height: ha = 13.94111573173
Height: hb = 13.01217468295
Height: hc = 8.13223417685

Median: ma = 18.74883332593
Median: mb = 18.15990197973
Median: mc = 8.15547532152

Inradius: r = 3.68325698574
Circumradius: R = 12.91114101436

Vertex coordinates: A[24; 0] B[0; 0] C[11.39658333333; 8.13223417685]
Centroid: CG[11.79986111111; 2.71107805895]
Coordinates of the circumscribed circle: U[12; -4.7654925172]
Coordinates of the inscribed circle: I[11.5; 3.68325698574]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.1699463901° = 147°10'10″ = 0.57330009501 rad
∠ B' = β' = 144.4877429573° = 144°29'15″ = 0.62198112798 rad
∠ C' = γ' = 68.34331065264° = 68°20'35″ = 1.94987804237 rad

Calculate another triangle


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+15+24 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-14)(26.5-15)(26.5-24) } ; ; T = sqrt{ 9523.44 } = 97.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.59 }{ 14 } = 13.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.59 }{ 15 } = 13.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.59 }{ 24 } = 8.13 ; ;

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{ 15**2+24**2-14**2 }{ 2 * 15 * 24 } ) = 32° 49'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+24**2-15**2 }{ 2 * 14 * 24 } ) = 35° 30'45" ; ;
 gamma = 180° - alpha - beta = 180° - 32° 49'50" - 35° 30'45" = 111° 39'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.59 }{ 26.5 } = 3.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 32° 49'50" } = 12.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 24**2 - 14**2 } }{ 2 } = 18.748 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 14**2 - 15**2 } }{ 2 } = 18.159 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 14**2 - 24**2 } }{ 2 } = 8.155 ; ;
Calculate another triangle


Look also our friend's collection of math examples and problems:

See more information about triangles or more details on solving triangles.