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?

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 = 200 ; ; b = 180 ; ; c = 322.87 ; ;

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 information about triangles or more details on solving triangles.