270 442.85 255 triangle

Obtuse scalene triangle.

Sides: a = 270   b = 442.85   c = 255

Area: T = 31200.04333315
Perimeter: p = 967.85
Semiperimeter: s = 483.925

Angle ∠ A = α = 33.54435977671° = 33°32'37″ = 0.5855446224 rad
Angle ∠ B = β = 114.9988433475° = 114°59'54″ = 2.00771012988 rad
Angle ∠ C = γ = 31.45879687577° = 31°27'29″ = 0.54990451308 rad

Height: ha = 231.1111432085
Height: hb = 140.906569417
Height: hc = 244.7066222208

Median: ma = 335.1879893863
Median: mb = 141.1865939013
Median: mc = 343.8787610859

Inradius: r = 64.4732890079
Circumradius: R = 244.312234098

Vertex coordinates: A[255; 0] B[0; 0] C[-114.1100240196; 244.7066222208]
Centroid: CG[46.96765866013; 81.56987407359]
Coordinates of the circumscribed circle: U[127.5; 208.4044102539]
Coordinates of the inscribed circle: I[41.075; 64.4732890079]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4566402233° = 146°27'23″ = 0.5855446224 rad
∠ B' = β' = 65.00215665248° = 65°6″ = 2.00771012988 rad
∠ C' = γ' = 148.5422031242° = 148°32'31″ = 0.54990451308 rad

Calculate another triangle




How did we calculate this triangle?

a = 270 ; ; b = 442.85 ; ; c = 255 ; ;

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

p = a+b+c = 270+442.85+255 = 967.85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 967.85 }{ 2 } = 483.93 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 483.93 * (483.93-270)(483.93-442.85)(483.93-255) } ; ; T = sqrt{ 973442703.89 } = 31200.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31200.04 }{ 270 } = 231.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31200.04 }{ 442.85 } = 140.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31200.04 }{ 255 } = 244.71 ; ;

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{ 270**2-442.85**2-255**2 }{ 2 * 442.85 * 255 } ) = 33° 32'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 442.85**2-270**2-255**2 }{ 2 * 270 * 255 } ) = 114° 59'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 255**2-270**2-442.85**2 }{ 2 * 442.85 * 270 } ) = 31° 27'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31200.04 }{ 483.93 } = 64.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 270 }{ 2 * sin 33° 32'37" } = 244.31 ; ;




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

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