24 25 30 triangle

Acute scalene triangle.

Sides: a = 24   b = 25   c = 30

Area: T = 290.4099086462
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 50.75328604588° = 50°45'10″ = 0.88658045198 rad
Angle ∠ B = β = 53.77439695691° = 53°46'26″ = 0.93985328208 rad
Angle ∠ C = γ = 75.47331699721° = 75°28'23″ = 1.31772553129 rad

Height: ha = 24.20107572052
Height: hb = 23.2332726917
Height: hc = 19.36106057642

Median: ma = 24.87696602309
Median: mb = 24.11994941904
Median: mc = 19.37878223751

Inradius: r = 7.35221287712
Circumradius: R = 15.49553829263

Vertex coordinates: A[30; 0] B[0; 0] C[14.18333333333; 19.36106057642]
Centroid: CG[14.72877777778; 6.45435352547]
Coordinates of the circumscribed circle: U[15; 3.88767585507]
Coordinates of the inscribed circle: I[14.5; 7.35221287712]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.2477139541° = 129°14'50″ = 0.88658045198 rad
∠ B' = β' = 126.2266030431° = 126°13'34″ = 0.93985328208 rad
∠ C' = γ' = 104.5276830028° = 104°31'37″ = 1.31772553129 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 = 24 ; ; b = 25 ; ; c = 30 ; ;

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

p = a+b+c = 24+25+30 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-24)(39.5-25)(39.5-30) } ; ; T = sqrt{ 84337.44 } = 290.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 290.41 }{ 24 } = 24.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 290.41 }{ 25 } = 23.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 290.41 }{ 30 } = 19.36 ; ;

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{ 24**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 50° 45'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 53° 46'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-24**2-25**2 }{ 2 * 25 * 24 } ) = 75° 28'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 290.41 }{ 39.5 } = 7.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 50° 45'10" } = 15.5 ; ;




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