170 162 12.6 triangle

Obtuse scalene triangle.

Sides: a = 170 b = 162 c = 12.6

Area: T = 807.379933086
Perimeter: p = 344.6
Semiperimeter: s = 172.3

Angle ∠ A = α = 127.713316306° = 127°42'47″ = 2.22990151935 rad
Angle ∠ B = β = 48.92554734874° = 48°55'32″ = 0.85439106005 rad
Angle ∠ C = γ = 3.36113634522° = 3°21'41″ = 0.05986668596 rad

Height: h_a = 9.49985803631
Height: h_b = 9.968764606
Height: h_c = 128.1555449343

Median: m_a = 77.30770501313
Median: m_b = 89.26657829182
Median: m_c = 165.9298629236

Inradius: r = 4.68658928082
Circumradius: R = 107.4487635435

Vertex coordinates: A[12.6; 0] B[0; 0] C[111.6976825397; 128.1555449343]
Centroid: CG[41.43222751323; 42.71884831143]
Coordinates of the circumscribed circle: U[6.3; 107.2632781805]
Coordinates of the inscribed circle: I[10.3; 4.68658928082]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 52.28768369396° = 52°17'13″ = 2.22990151935 rad
∠ B' = β' = 131.0754526513° = 131°4'28″ = 0.85439106005 rad
∠ C' = γ' = 176.6398636548° = 176°38'19″ = 0.05986668596 rad

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How did we calculate this triangle?

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

$p = a+b+c = 170+162+12.6 = 344.6 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 344.6 }{ 2 } = 172.3 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 172.3 * (172.3-170)(172.3-162)(172.3-12.6) } ; ; T = sqrt{ 651861.38 } = 807.38 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 807.38 }{ 170 } = 9.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 807.38 }{ 162 } = 9.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 807.38 }{ 12.6 } = 128.16 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 162**2+12.6**2-170**2 }{ 2 * 162 * 12.6 } ) = 127° 42'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 170**2+12.6**2-162**2 }{ 2 * 170 * 12.6 } ) = 48° 55'32" ; ; gamma = 180° - alpha - beta = 180° - 127° 42'47" - 48° 55'32" = 3° 21'41" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 807.38 }{ 172.3 } = 4.69 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin alpha } = fraction{ 170 }{ 2 * sin 127° 42'47" } = 107.45 ; ;$

8. Calculation of medians

$m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 162**2+2 * 12.6**2 - 170**2 } }{ 2 } = 77.307 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.6**2+2 * 170**2 - 162**2 } }{ 2 } = 89.266 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 162**2+2 * 170**2 - 12.6**2 } }{ 2 } = 165.929 ; ;$
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