Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 9   b = 10   c = 16

Area: T = 40.90876704299
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 30.75435198081° = 30°45'13″ = 0.53767501772 rad
Angle ∠ B = β = 34.62221618397° = 34°37'20″ = 0.60442707183 rad
Angle ∠ C = γ = 114.6244318352° = 114°37'28″ = 2.00105717581 rad

Height: ha = 9.09105934289
Height: hb = 8.1821534086
Height: hc = 5.11334588037

Median: ma = 12.56598566871
Median: mb = 11.97991485507
Median: mc = 5.14878150705

Inradius: r = 2.33875811674
Circumradius: R = 8.88003055715

Vertex coordinates: A[16; 0] B[0; 0] C[7.406625; 5.11334588037]
Centroid: CG[7.80220833333; 1.70444862679]
Coordinates of the circumscribed circle: U[8; -3.66767939881]
Coordinates of the inscribed circle: I[7.5; 2.33875811674]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.2466480192° = 149°14'47″ = 0.53767501772 rad
∠ B' = β' = 145.378783816° = 145°22'40″ = 0.60442707183 rad
∠ C' = γ' = 65.37656816478° = 65°22'32″ = 2.00105717581 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 = 9+10+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-9)(17.5-10)(17.5-16) } ; ; T = sqrt{ 1673.44 } = 40.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.91 }{ 9 } = 9.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.91 }{ 10 } = 8.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.91 }{ 16 } = 5.11 ; ;

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{ 10**2+16**2-9**2 }{ 2 * 10 * 16 } ) = 30° 45'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+16**2-10**2 }{ 2 * 9 * 16 } ) = 34° 37'20" ; ; gamma = 180° - alpha - beta = 180° - 30° 45'13" - 34° 37'20" = 114° 37'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.91 }{ 17.5 } = 2.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9 }{ 2 * sin 30° 45'13" } = 8.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 16**2 - 9**2 } }{ 2 } = 12.56 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 9**2 - 10**2 } }{ 2 } = 11.979 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 9**2 - 16**2 } }{ 2 } = 5.148 ; ;
Calculate another triangle

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

See more informations about triangles or more information about solving triangles.