4 7 8 triangle

Acute scalene triangle.

Sides: a = 4   b = 7   c = 8

Area: T = 13.99877676792
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 29.99547255274° = 29°59'41″ = 0.52435067187 rad
Angle ∠ B = β = 61.02884677763° = 61°1'42″ = 1.06551477001 rad
Angle ∠ C = γ = 88.97768066963° = 88°58'37″ = 1.55329382348 rad

Height: ha = 6.99988838396
Height: hb = 3.9999362194
Height: hc = 3.49994419198

Median: ma = 7.24656883731
Median: mb = 5.26878268764
Median: mc = 4.06220192023

Inradius: r = 1.47334492294
Circumradius: R = 4.00106379077

Vertex coordinates: A[8; 0] B[0; 0] C[1.93875; 3.49994419198]
Centroid: CG[3.31325; 1.16664806399]
Coordinates of the circumscribed circle: U[4; 0.07114399626]
Coordinates of the inscribed circle: I[2.5; 1.47334492294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0055274473° = 150°19″ = 0.52435067187 rad
∠ B' = β' = 118.9721532224° = 118°58'18″ = 1.06551477001 rad
∠ C' = γ' = 91.02331933037° = 91°1'23″ = 1.55329382348 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 = 4 ; ; b = 7 ; ; c = 8 ; ;

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

p = a+b+c = 4+7+8 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-4)(9.5-7)(9.5-8) } ; ; T = sqrt{ 195.94 } = 14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14 }{ 4 } = 7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14 }{ 7 } = 4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14 }{ 8 } = 3.5 ; ;

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{ 4**2-7**2-8**2 }{ 2 * 7 * 8 } ) = 29° 59'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-4**2-8**2 }{ 2 * 4 * 8 } ) = 61° 1'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-4**2-7**2 }{ 2 * 7 * 4 } ) = 88° 58'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14 }{ 9.5 } = 1.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 29° 59'41" } = 4 ; ;




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