200 180 322.87 triangle

Obtuse scalene triangle.

Sides: a = 200   b = 180   c = 322.87

Area: T = 16143.67883774
Perimeter: p = 702.87
Semiperimeter: s = 351.435

Angle ∠ A = α = 33.74994115973° = 33°44'58″ = 0.5899038353 rad
Angle ∠ B = β = 300.0003655147° = 30°1″ = 0.5243605155 rad
Angle ∠ C = γ = 116.2550222888° = 116°15'1″ = 2.02989491456 rad

Height: ha = 161.4376783774
Height: hb = 179.3744204193
Height: hc = 100.0011104949

Median: ma = 241.5010555797
Median: mb = 253.0276714894
Median: mc = 100.6911314298

Inradius: r = 45.93664558948
Circumradius: R = 179.9988011114

Vertex coordinates: A[322.87; 0] B[0; 0] C[173.204444281; 100.0011104949]
Centroid: CG[165.3588147603; 33.33437016495]
Coordinates of the circumscribed circle: U[161.435; -79.61217125815]
Coordinates of the inscribed circle: I[171.435; 45.93664558948]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2510588403° = 146°15'2″ = 0.5899038353 rad
∠ B' = β' = 1509.999634485° = 149°59'59″ = 0.5243605155 rad
∠ C' = γ' = 63.7549777112° = 63°44'59″ = 2.02989491456 rad

Calculate another triangle


How did we calculate this triangle?

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

p = a+b+c = 200+180+322.87 = 702.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 702.87 }{ 2 } = 351.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 351.44 * (351.44-200)(351.44-180)(351.44-322.87) } ; ; T = sqrt{ 260618351.55 } = 16143.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16143.68 }{ 200 } = 161.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16143.68 }{ 180 } = 179.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16143.68 }{ 322.87 } = 100 ; ;

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{ 180**2+322.87**2-200**2 }{ 2 * 180 * 322.87 } ) = 33° 44'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+322.87**2-180**2 }{ 2 * 200 * 322.87 } ) = 30° 1" ; ; gamma = 180° - alpha - beta = 180° - 33° 44'58" - 30° 1" = 116° 15'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16143.68 }{ 351.44 } = 45.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 33° 44'58" } = 180 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 322.87**2 - 200**2 } }{ 2 } = 241.501 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 322.87**2+2 * 200**2 - 180**2 } }{ 2 } = 253.027 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 200**2 - 322.87**2 } }{ 2 } = 100.691 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.