65 55 10.62 triangle

Obtuse scalene triangle.

Sides: a = 65   b = 55   c = 10.62

Area: T = 106.8454945808
Perimeter: p = 130.62
Semiperimeter: s = 65.31

Angle ∠ A = α = 158.5440423524° = 158°32'26″ = 2.7677052388 rad
Angle ∠ B = β = 18.03327704912° = 18°1'58″ = 0.31547312183 rad
Angle ∠ C = γ = 3.42768059845° = 3°25'37″ = 0.06598090473 rad

Height: ha = 3.28875367941
Height: hb = 3.88552707567
Height: hc = 20.1211458721

Median: ma = 22.64216033001
Median: mb = 37.5855132699
Median: mc = 59.97333599192

Inradius: r = 1.63659660972
Circumradius: R = 88.83655076432

Vertex coordinates: A[10.62; 0] B[0; 0] C[61.80771751412; 20.1211458721]
Centroid: CG[24.14223917137; 6.7077152907]
Coordinates of the circumscribed circle: U[5.31; 88.67766672707]
Coordinates of the inscribed circle: I[10.31; 1.63659660972]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 21.46595764758° = 21°27'34″ = 2.7677052388 rad
∠ B' = β' = 161.9677229509° = 161°58'2″ = 0.31547312183 rad
∠ C' = γ' = 176.5733194015° = 176°34'23″ = 0.06598090473 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 = 65 ; ; b = 55 ; ; c = 10.62 ; ;

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

p = a+b+c = 65+55+10.62 = 130.62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 130.62 }{ 2 } = 65.31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.31 * (65.31-65)(65.31-55)(65.31-10.62) } ; ; T = sqrt{ 11415.84 } = 106.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106.84 }{ 65 } = 3.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106.84 }{ 55 } = 3.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106.84 }{ 10.62 } = 20.12 ; ;

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{ 55**2+10.62**2-65**2 }{ 2 * 55 * 10.62 } ) = 158° 32'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 65**2+10.62**2-55**2 }{ 2 * 65 * 10.62 } ) = 18° 1'58" ; ;
 gamma = 180° - alpha - beta = 180° - 158° 32'26" - 18° 1'58" = 3° 25'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106.84 }{ 65.31 } = 1.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 65 }{ 2 * sin 158° 32'26" } = 88.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 10.62**2 - 65**2 } }{ 2 } = 22.642 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.62**2+2 * 65**2 - 55**2 } }{ 2 } = 37.585 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 65**2 - 10.62**2 } }{ 2 } = 59.973 ; ;
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.