9 10 15 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 10   c = 15

Area: T = 43.63548484585
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 35.57771025511° = 35°34'38″ = 0.62109375778 rad
Angle ∠ B = β = 40.274389294° = 40°16'26″ = 0.70329120344 rad
Angle ∠ C = γ = 104.1499004509° = 104°8'56″ = 1.81877430414 rad

Height: ha = 9.69766329908
Height: hb = 8.72769696917
Height: hc = 5.81879797945

Median: ma = 11.92768604419
Median: mb = 11.3143708499
Median: mc = 5.85223499554

Inradius: r = 2.56767557917
Circumradius: R = 7.73546435687

Vertex coordinates: A[15; 0] B[0; 0] C[6.86766666667; 5.81879797945]
Centroid: CG[7.28988888889; 1.93993265982]
Coordinates of the circumscribed circle: U[7.5; -1.89106906501]
Coordinates of the inscribed circle: I[7; 2.56767557917]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.4232897449° = 144°25'22″ = 0.62109375778 rad
∠ B' = β' = 139.726610706° = 139°43'34″ = 0.70329120344 rad
∠ C' = γ' = 75.85109954911° = 75°51'4″ = 1.81877430414 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 = 9 ; ; b = 10 ; ; c = 15 ; ;

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

p = a+b+c = 9+10+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 * (17-9)(17-10)(17-15) } ; ; T = sqrt{ 1904 } = 43.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.63 }{ 9 } = 9.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.63 }{ 10 } = 8.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.63 }{ 15 } = 5.82 ; ;

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{ 9**2-10**2-15**2 }{ 2 * 10 * 15 } ) = 35° 34'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-9**2-15**2 }{ 2 * 9 * 15 } ) = 40° 16'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-9**2-10**2 }{ 2 * 10 * 9 } ) = 104° 8'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.63 }{ 17 } = 2.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 35° 34'38" } = 7.73 ; ;




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