7 12 15 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 12   c = 15

Area: T = 41.23110562562
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 27.26660444507° = 27°15'58″ = 0.47658822497 rad
Angle ∠ B = β = 51.75333801217° = 51°45'12″ = 0.90332668822 rad
Angle ∠ C = γ = 100.9810575428° = 100°58'50″ = 1.76224435218 rad

Height: ha = 11.78803017875
Height: hb = 6.87218427094
Height: hc = 5.49774741675

Median: ma = 13.12444047484
Median: mb = 10.05498756211
Median: mc = 6.34442887702

Inradius: r = 2.42553562504
Circumradius: R = 7.64398721886

Vertex coordinates: A[15; 0] B[0; 0] C[4.33333333333; 5.49774741675]
Centroid: CG[6.44444444444; 1.83224913892]
Coordinates of the circumscribed circle: U[7.5; -1.45552137502]
Coordinates of the inscribed circle: I[5; 2.42553562504]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.7343955549° = 152°44'2″ = 0.47658822497 rad
∠ B' = β' = 128.2476619878° = 128°14'48″ = 0.90332668822 rad
∠ C' = γ' = 79.01994245724° = 79°1'10″ = 1.76224435218 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 = 12 ; ; c = 15 ; ;

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

p = a+b+c = 7+12+15 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-7)(17-12)(17-15) } ; ; T = sqrt{ 1700 } = 41.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.23 }{ 7 } = 11.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.23 }{ 12 } = 6.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.23 }{ 15 } = 5.5 ; ;

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{ 7**2-12**2-15**2 }{ 2 * 12 * 15 } ) = 27° 15'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-7**2-15**2 }{ 2 * 7 * 15 } ) = 51° 45'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-7**2-12**2 }{ 2 * 12 * 7 } ) = 100° 58'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.23 }{ 17 } = 2.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 27° 15'58" } = 7.64 ; ;




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