18.7 3.31 16.1 triangle

Obtuse scalene triangle.

Sides: a = 18.7   b = 3.31   c = 16.1

Area: T = 17.74106173314
Perimeter: p = 38.11
Semiperimeter: s = 19.055

Angle ∠ A = α = 138.256614632° = 138°15'22″ = 2.41330249644 rad
Angle ∠ B = β = 6.76880620617° = 6°46'5″ = 0.1188124967 rad
Angle ∠ C = γ = 34.97657916186° = 34°58'33″ = 0.61104427222 rad

Height: ha = 1.8977392228
Height: hb = 10.71994062425
Height: hc = 2.20438033952

Median: ma = 6.90436620717
Median: mb = 17.37698294465
Median: mc = 10.74880486601

Inradius: r = 0.9311021639
Circumradius: R = 14.04332218533

Vertex coordinates: A[16.1; 0] B[0; 0] C[18.57696863354; 2.20438033952]
Centroid: CG[11.55765621118; 0.73546011317]
Coordinates of the circumscribed circle: U[8.05; 11.50769361701]
Coordinates of the inscribed circle: I[15.745; 0.9311021639]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.74438536803° = 41°44'38″ = 2.41330249644 rad
∠ B' = β' = 173.2321937938° = 173°13'55″ = 0.1188124967 rad
∠ C' = γ' = 145.0244208381° = 145°1'27″ = 0.61104427222 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 = 18.7 ; ; b = 3.31 ; ; c = 16.1 ; ;

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

p = a+b+c = 18.7+3.31+16.1 = 38.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38.11 }{ 2 } = 19.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.06 * (19.06-18.7)(19.06-3.31)(19.06-16.1) } ; ; T = sqrt{ 314.73 } = 17.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.74 }{ 18.7 } = 1.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.74 }{ 3.31 } = 10.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.74 }{ 16.1 } = 2.2 ; ;

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{ 3.31**2+16.1**2-18.7**2 }{ 2 * 3.31 * 16.1 } ) = 138° 15'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.7**2+16.1**2-3.31**2 }{ 2 * 18.7 * 16.1 } ) = 6° 46'5" ; ;
 gamma = 180° - alpha - beta = 180° - 138° 15'22" - 6° 46'5" = 34° 58'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.74 }{ 19.06 } = 0.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.7 }{ 2 * sin 138° 15'22" } = 14.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.31**2+2 * 16.1**2 - 18.7**2 } }{ 2 } = 6.904 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.1**2+2 * 18.7**2 - 3.31**2 } }{ 2 } = 17.37 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.31**2+2 * 18.7**2 - 16.1**2 } }{ 2 } = 10.748 ; ;
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