8 15 16 triangle

Acute scalene triangle.

Sides: a = 8   b = 15   c = 16

Area: T = 59.4330106007
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 29.68662952314° = 29°41'11″ = 0.51881235945 rad
Angle ∠ B = β = 68.21769125021° = 68°13'1″ = 1.19106097287 rad
Angle ∠ C = γ = 82.09767922665° = 82°5'48″ = 1.43328593304 rad

Height: ha = 14.85875265017
Height: hb = 7.92440141343
Height: hc = 7.42987632509

Median: ma = 14.98333240638
Median: mb = 10.18657743937
Median: mc = 8.97221792225

Inradius: r = 3.04876977439
Circumradius: R = 8.07767145181

Vertex coordinates: A[16; 0] B[0; 0] C[2.969875; 7.42987632509]
Centroid: CG[6.32329166667; 2.4766254417]
Coordinates of the circumscribed circle: U[8; 1.11105482462]
Coordinates of the inscribed circle: I[4.5; 3.04876977439]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.3143704769° = 150°18'49″ = 0.51881235945 rad
∠ B' = β' = 111.7833087498° = 111°46'59″ = 1.19106097287 rad
∠ C' = γ' = 97.90332077335° = 97°54'12″ = 1.43328593304 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 = 8 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 8+15+16 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-8)(19.5-15)(19.5-16) } ; ; T = sqrt{ 3531.94 } = 59.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.43 }{ 8 } = 14.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.43 }{ 15 } = 7.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.43 }{ 16 } = 7.43 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 15**2+16**2-8**2 }{ 2 * 15 * 16 } ) = 29° 41'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+16**2-15**2 }{ 2 * 8 * 16 } ) = 68° 13'1" ; ; gamma = 180° - alpha - beta = 180° - 29° 41'11" - 68° 13'1" = 82° 5'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.43 }{ 19.5 } = 3.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 29° 41'11" } = 8.08 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 16**2 - 8**2 } }{ 2 } = 14.983 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 8**2 - 15**2 } }{ 2 } = 10.186 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 8**2 - 16**2 } }{ 2 } = 8.972 ; ;
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