4 15 15 triangle

Acute isosceles triangle.

Sides: a = 4   b = 15   c = 15

Area: T = 29.73221374946
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 15.32545113215° = 15°19'28″ = 0.26774631788 rad
Angle ∠ B = β = 82.33877443392° = 82°20'16″ = 1.43770647374 rad
Angle ∠ C = γ = 82.33877443392° = 82°20'16″ = 1.43770647374 rad

Height: ha = 14.86660687473
Height: hb = 3.96442849993
Height: hc = 3.96442849993

Median: ma = 14.86660687473
Median: mb = 8.01656097709
Median: mc = 8.01656097709

Inradius: r = 1.74989492644
Circumradius: R = 7.56875689325

Vertex coordinates: A[15; 0] B[0; 0] C[0.53333333333; 3.96442849993]
Centroid: CG[5.17877777778; 1.32114283331]
Coordinates of the circumscribed circle: U[7.5; 1.0099009191]
Coordinates of the inscribed circle: I[2; 1.74989492644]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6755488678° = 164°40'32″ = 0.26774631788 rad
∠ B' = β' = 97.66222556608° = 97°39'44″ = 1.43770647374 rad
∠ C' = γ' = 97.66222556608° = 97°39'44″ = 1.43770647374 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 = 4 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 4+15+15 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-4)(17-15)(17-15) } ; ; T = sqrt{ 884 } = 29.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.73 }{ 4 } = 14.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.73 }{ 15 } = 3.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.73 }{ 15 } = 3.96 ; ;

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{ 4**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 15° 19'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-4**2-15**2 }{ 2 * 4 * 15 } ) = 82° 20'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-4**2-15**2 }{ 2 * 15 * 4 } ) = 82° 20'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.73 }{ 17 } = 1.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 15° 19'28" } = 7.57 ; ;




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