158 185 201 triangle

Acute scalene triangle.

Sides: a = 158   b = 185   c = 201

Area: T = 13839.66882041
Perimeter: p = 544
Semiperimeter: s = 272

Angle ∠ A = α = 48.10548720485° = 48°6'18″ = 0.84395884035 rad
Angle ∠ B = β = 60.64216595114° = 60°38'30″ = 1.05883966223 rad
Angle ∠ C = γ = 71.25334684402° = 71°15'12″ = 1.24436076277 rad

Height: ha = 175.186567347
Height: hb = 149.6188034639
Height: hc = 137.7088141334

Median: ma = 176.2732516292
Median: mb = 155.326626951
Median: mc = 139.6221810617

Inradius: r = 50.88111331034
Circumradius: R = 106.1330253872

Vertex coordinates: A[201; 0] B[0; 0] C[77.46326865672; 137.7088141334]
Centroid: CG[92.82108955224; 45.90327137782]
Coordinates of the circumscribed circle: U[100.5; 34.10883682815]
Coordinates of the inscribed circle: I[87; 50.88111331034]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.8955127952° = 131°53'42″ = 0.84395884035 rad
∠ B' = β' = 119.3588340489° = 119°21'30″ = 1.05883966223 rad
∠ C' = γ' = 108.747653156° = 108°44'48″ = 1.24436076277 rad

Calculate another triangle




How did we calculate this triangle?

a = 158 ; ; b = 185 ; ; c = 201 ; ;

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

p = a+b+c = 158+185+201 = 544 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 544 }{ 2 } = 272 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 272 * (272-158)(272-185)(272-201) } ; ; T = sqrt{ 191536416 } = 13839.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13839.67 }{ 158 } = 175.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13839.67 }{ 185 } = 149.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13839.67 }{ 201 } = 137.71 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 158**2-185**2-201**2 }{ 2 * 185 * 201 } ) = 48° 6'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 185**2-158**2-201**2 }{ 2 * 158 * 201 } ) = 60° 38'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 201**2-158**2-185**2 }{ 2 * 185 * 158 } ) = 71° 15'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13839.67 }{ 272 } = 50.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 158 }{ 2 * sin 48° 6'18" } = 106.13 ; ;




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

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