Triangle calculator

You have entered side a, c and angle β.

Acute scalene triangle.

Sides: a = 125 b = 87.43435383235 c = 140

Area: T = 5387.03879091
Perimeter: p = 352.4343538323
Semiperimeter: s = 176.2176769162

Angle ∠ A = α = 61.66546816852° = 61°39'53″ = 1.07662517276 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 80.33553183148° = 80°20'7″ = 1.40221158102 rad

Height: h_a = 86.19326065456
Height: h_b = 123.2265892773
Height: h_c = 76.95876844157

Median: m_a = 98.57700857861
Median: m_b = 125.3055004266
Median: m_c = 82.06658992023

Inradius: r = 30.57105179747
Circumradius: R = 71.00878036613

Vertex coordinates: A[140; 0] B[0; 0] C[98.50113442008; 76.95876844157]
Centroid: CG[79.55004480669; 25.65325614719]
Coordinates of the circumscribed circle: U[70; 11.92109135892]
Coordinates of the inscribed circle: I[88.78332308383; 30.57105179747]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.3355318315° = 118°20'7″ = 1.07662517276 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 99.66546816852° = 99°39'53″ = 1.40221158102 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.

$a = 125 ; ; b = 87.43 ; ; c = 140 ; ;$

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

$p = a+b+c = 125+87.43+140 = 352.43 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 352.43 }{ 2 } = 176.22 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 176.22 * (176.22-125)(176.22-87.43)(176.22-140) } ; ; T = sqrt{ 29020177.43 } = 5387.04 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5387.04 }{ 125 } = 86.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5387.04 }{ 87.43 } = 123.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5387.04 }{ 140 } = 76.96 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 125**2-87.43**2-140**2 }{ 2 * 87.43 * 140 } ) = 61° 39'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 87.43**2-125**2-140**2 }{ 2 * 125 * 140 } ) = 38° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 140**2-125**2-87.43**2 }{ 2 * 87.43 * 125 } ) = 80° 20'7" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 5387.04 }{ 176.22 } = 30.57 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 125 }{ 2 * sin 61° 39'53" } = 71.01 ; ;$

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