31 96 90 triangle

Obtuse scalene triangle.

Sides: a = 31   b = 96   c = 90

Area: T = 1394.46217017
Perimeter: p = 217
Semiperimeter: s = 108.5

Angle ∠ A = α = 18.83218611872° = 18°49'55″ = 0.3298677982 rad
Angle ∠ B = β = 91.59217541766° = 91°35'30″ = 1.59985776781 rad
Angle ∠ C = γ = 69.57663846362° = 69°34'35″ = 1.21443369935 rad

Height: ha = 89.96552710772
Height: hb = 29.0511285452
Height: hc = 30.98880378155

Median: ma = 91.74882969869
Median: mb = 47.18658029496
Median: mc = 55.34988933945

Inradius: r = 12.85221815825
Circumradius: R = 48.01985292421

Vertex coordinates: A[90; 0] B[0; 0] C[-0.86111111111; 30.98880378155]
Centroid: CG[29.7132962963; 10.32993459385]
Coordinates of the circumscribed circle: U[45; 16.75664659335]
Coordinates of the inscribed circle: I[12.5; 12.85221815825]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.1688138813° = 161°10'5″ = 0.3298677982 rad
∠ B' = β' = 88.40882458234° = 88°24'30″ = 1.59985776781 rad
∠ C' = γ' = 110.4243615364° = 110°25'25″ = 1.21443369935 rad

Calculate another triangle




How did we calculate this triangle?

a = 31 ; ; b = 96 ; ; c = 90 ; ;

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

p = a+b+c = 31+96+90 = 217 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 217 }{ 2 } = 108.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 108.5 * (108.5-31)(108.5-96)(108.5-90) } ; ; T = sqrt{ 1944523.44 } = 1394.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1394.46 }{ 31 } = 89.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1394.46 }{ 96 } = 29.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1394.46 }{ 90 } = 30.99 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 31**2-96**2-90**2 }{ 2 * 96 * 90 } ) = 18° 49'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 96**2-31**2-90**2 }{ 2 * 31 * 90 } ) = 91° 35'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 90**2-31**2-96**2 }{ 2 * 96 * 31 } ) = 69° 34'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1394.46 }{ 108.5 } = 12.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 31 }{ 2 * sin 18° 49'55" } = 48.02 ; ;




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

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