Triangle calculator

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 105 b = 38 c = 133

Area: T = 1508.97331608
Perimeter: p = 276
Semiperimeter: s = 138

Angle ∠ A = α = 36.66553494337° = 36°39'55″ = 0.6439931069 rad
Angle ∠ B = β = 12.48105313632° = 12°28'50″ = 0.21878263647 rad
Angle ∠ C = γ = 130.8544119203° = 130°51'15″ = 2.28438352199 rad

Height: h_a = 28.74223459199
Height: h_b = 79.42196400418
Height: h_c = 22.69113257262

Median: m_a = 82.52442388635
Median: m_b = 118.3054691369
Median: m_c = 42.57105297125

Inradius: r = 10.93545881217
Circumradius: R = 87.91990587658

Vertex coordinates: A[133; 0] B[0; 0] C[102.5198796993; 22.69113257262]
Centroid: CG[78.50662656642; 7.56437752421]
Coordinates of the circumscribed circle: U[66.5; -57.51109632528]
Coordinates of the inscribed circle: I[100; 10.93545881217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.3354650566° = 143°20'5″ = 0.6439931069 rad
∠ B' = β' = 167.5199468637° = 167°31'10″ = 0.21878263647 rad
∠ C' = γ' = 49.14658807969° = 49°8'45″ = 2.28438352199 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.

$a = 105 ; ; b = 38 ; ; c = 133 ; ;$

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

$p = a+b+c = 105+38+133 = 276 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 276 }{ 2 } = 138 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 138 * (138-105)(138-38)(138-133) } ; ; T = sqrt{ 2277000 } = 1508.97 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1508.97 }{ 105 } = 28.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1508.97 }{ 38 } = 79.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1508.97 }{ 133 } = 22.69 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 105**2-38**2-133**2 }{ 2 * 38 * 133 } ) = 36° 39'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 38**2-105**2-133**2 }{ 2 * 105 * 133 } ) = 12° 28'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 133**2-105**2-38**2 }{ 2 * 38 * 105 } ) = 130° 51'15" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 1508.97 }{ 138 } = 10.93 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 105 }{ 2 * sin 36° 39'55" } = 87.92 ; ;$

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

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