7 10 15 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 10   c = 15

Area: T = 29.39438769134
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ C = γ = 122.8788349564° = 122°52'42″ = 2.14546317793 rad

Height: ha = 8.39882505467
Height: hb = 5.87987753827
Height: hc = 3.91991835885

Median: ma = 12.25876506721
Median: mb = 10.58330052443
Median: mc = 4.27220018727

Inradius: r = 1.83771173071
Circumradius: R = 8.93304313539

Vertex coordinates: A[15; 0] B[0; 0] C[5.8; 3.91991835885]
Centroid: CG[6.93333333333; 1.30663945295]
Coordinates of the circumscribed circle: U[7.5; -4.84879484493]
Coordinates of the inscribed circle: I[6; 1.83771173071]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ C' = γ' = 57.12216504356° = 57°7'18″ = 2.14546317793 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 = 10 ; ; c = 15 ; ;

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

p = a+b+c = 7+10+15 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-7)(16-10)(16-15) } ; ; T = sqrt{ 864 } = 29.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.39 }{ 7 } = 8.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.39 }{ 10 } = 5.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.39 }{ 15 } = 3.92 ; ;

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**2-10**2-15**2 }{ 2 * 10 * 15 } ) = 23° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-7**2-15**2 }{ 2 * 7 * 15 } ) = 34° 2'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-7**2-10**2 }{ 2 * 10 * 7 } ) = 122° 52'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.39 }{ 16 } = 1.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 23° 4'26" } = 8.93 ; ;




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