116 100 16.42 triangle

Obtuse scalene triangle.

Sides: a = 116   b = 100   c = 16.42

Area: T = 198.6865611213
Perimeter: p = 232.42
Semiperimeter: s = 116.21

Angle ∠ A = α = 165.9955128164° = 165°59'42″ = 2.89771615287 rad
Angle ∠ B = β = 12.04217555239° = 12°2'30″ = 0.21101682816 rad
Angle ∠ C = γ = 1.96331163117° = 1°57'47″ = 0.03442628432 rad

Height: ha = 3.42656139864
Height: hb = 3.97437122243
Height: hc = 24.22004398555

Median: ma = 42.0810971947
Median: mb = 66.05215571353
Median: mc = 107.9844239128

Inradius: r = 1.71097118253
Circumradius: R = 239.6655065373

Vertex coordinates: A[16.42; 0] B[0; 0] C[113.4487515225; 24.22004398555]
Centroid: CG[43.28991717418; 8.06768132852]
Coordinates of the circumscribed circle: U[8.21; 239.524440264]
Coordinates of the inscribed circle: I[16.21; 1.71097118253]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 14.00548718356° = 14°18″ = 2.89771615287 rad
∠ B' = β' = 167.9588244476° = 167°57'30″ = 0.21101682816 rad
∠ C' = γ' = 178.0376883688° = 178°2'13″ = 0.03442628432 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 = 116 ; ; b = 100 ; ; c = 16.42 ; ;

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

p = a+b+c = 116+100+16.42 = 232.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 232.42 }{ 2 } = 116.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 116.21 * (116.21-116)(116.21-100)(116.21-16.42) } ; ; T = sqrt{ 39475.97 } = 198.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 198.69 }{ 116 } = 3.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 198.69 }{ 100 } = 3.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 198.69 }{ 16.42 } = 24.2 ; ;

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{ 100**2+16.42**2-116**2 }{ 2 * 100 * 16.42 } ) = 165° 59'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 116**2+16.42**2-100**2 }{ 2 * 116 * 16.42 } ) = 12° 2'30" ; ;
 gamma = 180° - alpha - beta = 180° - 165° 59'42" - 12° 2'30" = 1° 57'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 198.69 }{ 116.21 } = 1.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 116 }{ 2 * sin 165° 59'42" } = 239.67 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 16.42**2 - 116**2 } }{ 2 } = 42.081 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.42**2+2 * 116**2 - 100**2 } }{ 2 } = 66.052 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 116**2 - 16.42**2 } }{ 2 } = 107.984 ; ;
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.