17 30 30 triangle

Acute isosceles triangle.

Sides: a = 17   b = 30   c = 30

Area: T = 244.5550480474
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 32.91884992565° = 32°55'7″ = 0.57545361968 rad
Angle ∠ B = β = 73.54107503717° = 73°32'27″ = 1.28435282284 rad
Angle ∠ C = γ = 73.54107503717° = 73°32'27″ = 1.28435282284 rad

Height: ha = 28.77106447616
Height: hb = 16.30333653649
Height: hc = 16.30333653649

Median: ma = 28.77106447616
Median: mb = 19.22223827867
Median: mc = 19.22223827867

Inradius: r = 6.35219605318
Circumradius: R = 15.64109424859

Vertex coordinates: A[30; 0] B[0; 0] C[4.81766666667; 16.30333653649]
Centroid: CG[11.60655555556; 5.43444551216]
Coordinates of the circumscribed circle: U[15; 4.4321600371]
Coordinates of the inscribed circle: I[8.5; 6.35219605318]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.0821500743° = 147°4'53″ = 0.57545361968 rad
∠ B' = β' = 106.4599249628° = 106°27'33″ = 1.28435282284 rad
∠ C' = γ' = 106.4599249628° = 106°27'33″ = 1.28435282284 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 = 17 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 17+30+30 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-17)(38.5-30)(38.5-30) } ; ; T = sqrt{ 59804.94 } = 244.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 244.55 }{ 17 } = 28.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 244.55 }{ 30 } = 16.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 244.55 }{ 30 } = 16.3 ; ;

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{ 17**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 32° 55'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 73° 32'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-30**2 }{ 2 * 30 * 17 } ) = 73° 32'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 244.55 }{ 38.5 } = 6.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 32° 55'7" } = 15.64 ; ;




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