15 16 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 30

Area: T = 58.54443208177
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 14.11988847899° = 14°7'8″ = 0.24664210263 rad
Angle ∠ B = β = 15.08217506421° = 15°4'54″ = 0.26332262057 rad
Angle ∠ C = γ = 150.7999364568° = 150°47'58″ = 2.63219454216 rad

Height: ha = 7.80659094424
Height: hb = 7.31880401022
Height: hc = 3.90329547212

Median: ma = 22.8421847561
Median: mb = 22.32771135618
Median: mc = 3.9377003937

Inradius: r = 1.91994859284
Circumradius: R = 30.74659370074

Vertex coordinates: A[30; 0] B[0; 0] C[14.48333333333; 3.90329547212]
Centroid: CG[14.82877777778; 1.30109849071]
Coordinates of the circumscribed circle: U[15; -26.8398640846]
Coordinates of the inscribed circle: I[14.5; 1.91994859284]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.881111521° = 165°52'52″ = 0.24664210263 rad
∠ B' = β' = 164.9188249358° = 164°55'6″ = 0.26332262057 rad
∠ C' = γ' = 29.2010635432° = 29°12'2″ = 2.63219454216 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 = 16 ; ; c = 30 ; ;

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

p = a+b+c = 15+16+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-15)(30.5-16)(30.5-30) } ; ; T = sqrt{ 3427.44 } = 58.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.54 }{ 15 } = 7.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.54 }{ 16 } = 7.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.54 }{ 30 } = 3.9 ; ;

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**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 14° 7'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 15° 4'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-16**2 }{ 2 * 16 * 15 } ) = 150° 47'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.54 }{ 30.5 } = 1.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 14° 7'8" } = 30.75 ; ;




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