7 23 25 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 23   c = 25

Area: T = 79.6387852181
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 16.08113096745° = 16°4'53″ = 0.28106718019 rad
Angle ∠ B = β = 65.52656574372° = 65°31'32″ = 1.14436384668 rad
Angle ∠ C = γ = 98.39330328884° = 98°23'35″ = 1.71772823849 rad

Height: ha = 22.75436720517
Height: hb = 6.92550306244
Height: hc = 6.37110281745

Median: ma = 23.76444692766
Median: mb = 14.30990880213
Median: mc = 11.52217186218

Inradius: r = 2.89659218975
Circumradius: R = 12.63553231842

Vertex coordinates: A[25; 0] B[0; 0] C[2.9; 6.37110281745]
Centroid: CG[9.3; 2.12436760582]
Coordinates of the circumscribed circle: U[12.5; -1.84442863033]
Coordinates of the inscribed circle: I[4.5; 2.89659218975]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.9198690326° = 163°55'7″ = 0.28106718019 rad
∠ B' = β' = 114.4744342563° = 114°28'28″ = 1.14436384668 rad
∠ C' = γ' = 81.60769671116° = 81°36'25″ = 1.71772823849 rad

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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 = 23 ; ; c = 25 ; ;

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

p = a+b+c = 7+23+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-7)(27.5-23)(27.5-25) } ; ; T = sqrt{ 6342.19 } = 79.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.64 }{ 7 } = 22.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.64 }{ 23 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.64 }{ 25 } = 6.37 ; ;

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**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 16° 4'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 65° 31'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-23**2 }{ 2 * 23 * 7 } ) = 98° 23'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.64 }{ 27.5 } = 2.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 4'53" } = 12.64 ; ;




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