7 25 30 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 25   c = 30

Area: T = 66.8133172354
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 10.26330958986° = 10°15'47″ = 0.17991248149 rad
Angle ∠ B = β = 39.51876527972° = 39°31'4″ = 0.6989713154 rad
Angle ∠ C = γ = 130.2199251304° = 130°13'9″ = 2.27327546847 rad

Height: ha = 19.08994778154
Height: hb = 5.34550537883
Height: hc = 4.45442114903

Median: ma = 27.39106918496
Median: mb = 17.84395627749
Median: mc = 10.58330052443

Inradius: r = 2.15552636243
Circumradius: R = 19.64443299092

Vertex coordinates: A[30; 0] B[0; 0] C[5.4; 4.45442114903]
Centroid: CG[11.8; 1.48547371634]
Coordinates of the circumscribed circle: U[15; -12.68546244556]
Coordinates of the inscribed circle: I[6; 2.15552636243]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.7376904101° = 169°44'13″ = 0.17991248149 rad
∠ B' = β' = 140.4822347203° = 140°28'56″ = 0.6989713154 rad
∠ C' = γ' = 49.78107486958° = 49°46'51″ = 2.27327546847 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 7+25+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-7)(31-25)(31-30) } ; ; T = sqrt{ 4464 } = 66.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.81 }{ 7 } = 19.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.81 }{ 25 } = 5.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.81 }{ 30 } = 4.45 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 10° 15'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-7**2-30**2 }{ 2 * 7 * 30 } ) = 39° 31'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-7**2-25**2 }{ 2 * 25 * 7 } ) = 130° 13'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.81 }{ 31 } = 2.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 10° 15'47" } = 19.64 ; ;




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