Triangle calculator

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 96 b = 98 c = 35

Area: T = 1666.918764569
Perimeter: p = 229
Semiperimeter: s = 114.5

Angle ∠ A = α = 76.40106435867° = 76°24'2″ = 1.33334427812 rad
Angle ∠ B = β = 82.84550241662° = 82°50'42″ = 1.44659184406 rad
Angle ∠ C = γ = 20.75443322471° = 20°45'16″ = 0.36222314318 rad

Height: h_a = 34.72774509518
Height: h_b = 34.0198727463
Height: h_c = 95.25224368964

Median: m_a = 55.77218567021
Median: m_b = 53.09989642084
Median: m_c = 95.41435734579

Inradius: r = 14.55882327134
Circumradius: R = 49.38545633064

Vertex coordinates: A[35; 0] B[0; 0] C[11.95771428571; 95.25224368964]
Centroid: CG[15.65223809524; 31.75108122988]
Coordinates of the circumscribed circle: U[17.5; 46.18799208852]
Coordinates of the inscribed circle: I[16.5; 14.55882327134]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.5999356413° = 103°35'58″ = 1.33334427812 rad
∠ B' = β' = 97.15549758338° = 97°9'18″ = 1.44659184406 rad
∠ C' = γ' = 159.2465667753° = 159°14'44″ = 0.36222314318 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.

$a = 96 ; ; b = 98 ; ; c = 35 ; ;$

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

$p = a+b+c = 96+98+35 = 229 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 229 }{ 2 } = 114.5 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 114.5 * (114.5-96)(114.5-98)(114.5-35) } ; ; T = sqrt{ 2778614.44 } = 1666.92 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1666.92 }{ 96 } = 34.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1666.92 }{ 98 } = 34.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1666.92 }{ 35 } = 95.25 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 96**2-98**2-35**2 }{ 2 * 98 * 35 } ) = 76° 24'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 98**2-96**2-35**2 }{ 2 * 96 * 35 } ) = 82° 50'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 35**2-96**2-98**2 }{ 2 * 98 * 96 } ) = 20° 45'16" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 1666.92 }{ 114.5 } = 14.56 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 96 }{ 2 * sin 76° 24'2" } = 49.38 ; ;$

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