10 10 17 triangle

Obtuse isosceles triangle.

Sides: a = 10   b = 10   c = 17

Area: T = 44.77765284496
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ B = β = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ C = γ = 116.4233338766° = 116°25'24″ = 2.03219705876 rad

Height: ha = 8.95553056899
Height: hb = 8.95553056899
Height: hc = 5.26878268764

Median: ma = 13.01992165663
Median: mb = 13.01992165663
Median: mc = 5.26878268764

Inradius: r = 2.42203528892
Circumradius: R = 9.49215799575

Vertex coordinates: A[17; 0] B[0; 0] C[8.5; 5.26878268764]
Centroid: CG[8.5; 1.75659422921]
Coordinates of the circumscribed circle: U[8.5; -4.22437530811]
Coordinates of the inscribed circle: I[8.5; 2.42203528892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ B' = β' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ C' = γ' = 63.57766612341° = 63°34'36″ = 2.03219705876 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 = 10 ; ; c = 17 ; ;

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

p = a+b+c = 10+10+17 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-10)(18.5-10)(18.5-17) } ; ; T = sqrt{ 2004.94 } = 44.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.78 }{ 10 } = 8.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.78 }{ 10 } = 8.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.78 }{ 17 } = 5.27 ; ;

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**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 31° 47'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 31° 47'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-10**2-10**2 }{ 2 * 10 * 10 } ) = 116° 25'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.78 }{ 18.5 } = 2.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 31° 47'18" } = 9.49 ; ;




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