11 15 15 triangle

Acute isosceles triangle.

Sides: a = 11   b = 15   c = 15

Area: T = 76.75440715532
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 43.02203765338° = 43°1'13″ = 0.7510847216 rad
Angle ∠ B = β = 68.49898117331° = 68°29'23″ = 1.19553727188 rad
Angle ∠ C = γ = 68.49898117331° = 68°29'23″ = 1.19553727188 rad

Height: ha = 13.9555285737
Height: hb = 10.23438762071
Height: hc = 10.23438762071

Median: ma = 13.9555285737
Median: mb = 10.80550913925
Median: mc = 10.80550913925

Inradius: r = 3.74441010514
Circumradius: R = 8.06114615939

Vertex coordinates: A[15; 0] B[0; 0] C[4.03333333333; 10.23438762071]
Centroid: CG[6.34444444444; 3.4111292069]
Coordinates of the circumscribed circle: U[7.5; 2.95658692511]
Coordinates of the inscribed circle: I[5.5; 3.74441010514]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.9879623466° = 136°58'47″ = 0.7510847216 rad
∠ B' = β' = 111.5110188267° = 111°30'37″ = 1.19553727188 rad
∠ C' = γ' = 111.5110188267° = 111°30'37″ = 1.19553727188 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 = 11 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 11+15+15 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-11)(20.5-15)(20.5-15) } ; ; T = sqrt{ 5891.19 } = 76.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.75 }{ 11 } = 13.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.75 }{ 15 } = 10.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.75 }{ 15 } = 10.23 ; ;

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{ 11**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 43° 1'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-15**2 }{ 2 * 11 * 15 } ) = 68° 29'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 68° 29'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.75 }{ 20.5 } = 3.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 43° 1'13" } = 8.06 ; ;




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