15 15 17 triangle

Acute isosceles triangle.

Sides: a = 15   b = 15   c = 17

Area: T = 105.0533260302
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 55.48218921589° = 55°28'55″ = 0.96883416934 rad
Angle ∠ B = β = 55.48218921589° = 55°28'55″ = 0.96883416934 rad
Angle ∠ C = γ = 69.03662156821° = 69°2'10″ = 1.20549092668 rad

Height: ha = 14.00771013735
Height: hb = 14.00771013735
Height: hc = 12.35992070943

Median: ma = 14.16986273153
Median: mb = 14.16986273153
Median: mc = 12.35992070943

Inradius: r = 4.47703515022
Circumradius: R = 9.10325256832

Vertex coordinates: A[17; 0] B[0; 0] C[8.5; 12.35992070943]
Centroid: CG[8.5; 4.12197356981]
Coordinates of the circumscribed circle: U[8.5; 3.25766814111]
Coordinates of the inscribed circle: I[8.5; 4.47703515022]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.5188107841° = 124°31'5″ = 0.96883416934 rad
∠ B' = β' = 124.5188107841° = 124°31'5″ = 0.96883416934 rad
∠ C' = γ' = 110.9643784318° = 110°57'50″ = 1.20549092668 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 = 15 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 15+15+17 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-15)(23.5-15)(23.5-17) } ; ; T = sqrt{ 11036.19 } = 105.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 105.05 }{ 15 } = 14.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 105.05 }{ 15 } = 14.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 105.05 }{ 17 } = 12.36 ; ;

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{ 15**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 55° 28'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 55° 28'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 69° 2'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 105.05 }{ 23.5 } = 4.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 55° 28'55" } = 9.1 ; ;




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