Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

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: ha = 34.72774509518
Height: hb = 34.0198727463
Height: hc = 95.25224368964

Median: ma = 55.77218567021
Median: mb = 53.09989642084
Median: mc = 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

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

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


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 ; ; : Nr. 1

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

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

3. Semiperimeter of the triangle

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

4. 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 ; ;

5. 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 ; ;

6. 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{ 98**2+35**2-96**2 }{ 2 * 98 * 35 } ) = 76° 24'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 96**2+35**2-98**2 }{ 2 * 96 * 35 } ) = 82° 50'42" ; ; gamma = 180° - alpha - beta = 180° - 76° 24'2" - 82° 50'42" = 20° 45'16" ; ;

7. Inradius

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

8. Circumradius

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

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 98**2+2 * 35**2 - 96**2 } }{ 2 } = 55.772 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 96**2 - 98**2 } }{ 2 } = 53.099 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 98**2+2 * 96**2 - 35**2 } }{ 2 } = 95.414 ; ;
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