10 15 17 triangle

Acute scalene triangle.

Sides: a = 10   b = 15   c = 17

Area: T = 74.45880418759
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 35.731129198° = 35°43'53″ = 0.6243628691 rad
Angle ∠ B = β = 61.16108105994° = 61°9'39″ = 1.06774575181 rad
Angle ∠ C = γ = 83.10878974207° = 83°6'28″ = 1.45105064444 rad

Height: ha = 14.89216083752
Height: hb = 9.92877389168
Height: hc = 8.76597696325

Median: ma = 15.23215462117
Median: mb = 11.75879760163
Median: mc = 9.5

Inradius: r = 3.54656210417
Circumradius: R = 8.56218689928

Vertex coordinates: A[17; 0] B[0; 0] C[4.82435294118; 8.76597696325]
Centroid: CG[7.27545098039; 2.92199232108]
Coordinates of the circumscribed circle: U[8.5; 1.02774242791]
Coordinates of the inscribed circle: I[6; 3.54656210417]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.269870802° = 144°16'7″ = 0.6243628691 rad
∠ B' = β' = 118.8399189401° = 118°50'21″ = 1.06774575181 rad
∠ C' = γ' = 96.89221025793° = 96°53'32″ = 1.45105064444 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 = 10 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 10+15+17 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-10)(21-15)(21-17) } ; ; T = sqrt{ 5544 } = 74.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.46 }{ 10 } = 14.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.46 }{ 15 } = 9.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.46 }{ 17 } = 8.76 ; ;

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{ 10**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 35° 43'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 61° 9'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-10**2-15**2 }{ 2 * 15 * 10 } ) = 83° 6'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.46 }{ 21 } = 3.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 35° 43'53" } = 8.56 ; ;




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