10 11 16 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 11   c = 16

Area: T = 54.32995165724
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 38.11002974907° = 38°6'1″ = 0.66549756372 rad
Angle ∠ B = β = 42.74655692247° = 42°44'44″ = 0.74660509236 rad
Angle ∠ C = γ = 99.15441332846° = 99°9'15″ = 1.73105660928 rad

Height: ha = 10.86599033145
Height: hb = 9.87326393768
Height: hc = 6.78774395716

Median: ma = 12.78767118525
Median: mb = 12.15552457811
Median: mc = 6.81990908485

Inradius: r = 2.93551090039
Circumradius: R = 8.10332028971

Vertex coordinates: A[16; 0] B[0; 0] C[7.344375; 6.78774395716]
Centroid: CG[7.781125; 2.26224798572]
Coordinates of the circumscribed circle: U[8; -1.28991459154]
Coordinates of the inscribed circle: I[7.5; 2.93551090039]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.9899702509° = 141°53'59″ = 0.66549756372 rad
∠ B' = β' = 137.2544430775° = 137°15'16″ = 0.74660509236 rad
∠ C' = γ' = 80.84658667154° = 80°50'45″ = 1.73105660928 rad

Calculate another triangle




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 10 ; ; b = 11 ; ; c = 16 ; ;

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

p = a+b+c = 10+11+16 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-10)(18.5-11)(18.5-16) } ; ; T = sqrt{ 2948.44 } = 54.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.3 }{ 10 } = 10.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.3 }{ 11 } = 9.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.3 }{ 16 } = 6.79 ; ;

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{ 10**2-11**2-16**2 }{ 2 * 11 * 16 } ) = 38° 6'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-10**2-16**2 }{ 2 * 10 * 16 } ) = 42° 44'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-10**2-11**2 }{ 2 * 11 * 10 } ) = 99° 9'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.3 }{ 18.5 } = 2.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 38° 6'1" } = 8.1 ; ;




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

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