7 20 25 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 20   c = 25

Area: T = 54.44326303553
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 12.57881186558° = 12°34'41″ = 0.22195295842 rad
Angle ∠ B = β = 38.47770777501° = 38°28'37″ = 0.67215516933 rad
Angle ∠ C = γ = 128.9454803594° = 128°56'41″ = 2.25105113761 rad

Height: ha = 15.55550372444
Height: hb = 5.44442630355
Height: hc = 4.35554104284

Median: ma = 22.36662692463
Median: mb = 15.39548043183
Median: mc = 8.26113558209

Inradius: r = 2.09439473214
Circumradius: R = 16.07219640894

Vertex coordinates: A[25; 0] B[0; 0] C[5.48; 4.35554104284]
Centroid: CG[10.16; 1.45218034761]
Coordinates of the circumscribed circle: U[12.5; -10.10223774276]
Coordinates of the inscribed circle: I[6; 2.09439473214]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.4221881344° = 167°25'19″ = 0.22195295842 rad
∠ B' = β' = 141.523292225° = 141°31'23″ = 0.67215516933 rad
∠ C' = γ' = 51.05551964059° = 51°3'19″ = 2.25105113761 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 = 7 ; ; b = 20 ; ; c = 25 ; ;

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

p = a+b+c = 7+20+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-7)(26-20)(26-25) } ; ; T = sqrt{ 2964 } = 54.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.44 }{ 7 } = 15.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.44 }{ 20 } = 5.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.44 }{ 25 } = 4.36 ; ;

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{ 7**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 12° 34'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 38° 28'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-20**2 }{ 2 * 20 * 7 } ) = 128° 56'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.44 }{ 26 } = 2.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 12° 34'41" } = 16.07 ; ;




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