Triangle calculator

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

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 36.4   b = 36.4   c = 45.8

Area: T = 647.932242356
Perimeter: p = 118.6
Semiperimeter: s = 59.3

Angle ∠ A = α = 51.01547076665° = 51°53″ = 0.89903746157 rad
Angle ∠ B = β = 51.01547076665° = 51°53″ = 0.89903746157 rad
Angle ∠ C = γ = 77.97105846669° = 77°58'14″ = 1.36108434221 rad

Height: ha = 35.60106826132
Height: hb = 35.60106826132
Height: hc = 28.29439922952

Median: ma = 37.14991588061
Median: mb = 37.14991588061
Median: mc = 28.29439922952

Inradius: r = 10.92663477835
Circumradius: R = 23.41441577862

Vertex coordinates: A[45.8; 0] B[0; 0] C[22.9; 28.29439922952]
Centroid: CG[22.9; 9.43113307651]
Coordinates of the circumscribed circle: U[22.9; 4.8879834509]
Coordinates of the inscribed circle: I[22.9; 10.92663477835]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.9855292333° = 128°59'7″ = 0.89903746157 rad
∠ B' = β' = 128.9855292333° = 128°59'7″ = 0.89903746157 rad
∠ C' = γ' = 102.0299415333° = 102°1'46″ = 1.36108434221 rad

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How did we calculate this triangle?

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

a = 36.4 ; ; b = 36.4 ; ; c = 45.8 ; ;


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 = 36.4 ; ; b = 36.4 ; ; c = 45.8 ; ; : Nr. 1

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

p = a+b+c = 36.4+36.4+45.8 = 118.6 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.6 }{ 2 } = 59.3 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.3 * (59.3-36.4)(59.3-36.4)(59.3-45.8) } ; ; T = sqrt{ 419816.43 } = 647.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 647.93 }{ 36.4 } = 35.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 647.93 }{ 36.4 } = 35.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 647.93 }{ 45.8 } = 28.29 ; ;

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{ 36.4**2+45.8**2-36.4**2 }{ 2 * 36.4 * 45.8 } ) = 51° 53" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 36.4**2+45.8**2-36.4**2 }{ 2 * 36.4 * 45.8 } ) = 51° 53" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 36.4**2+36.4**2-45.8**2 }{ 2 * 36.4 * 36.4 } ) = 77° 58'14" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 647.93 }{ 59.3 } = 10.93 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 36.4 }{ 2 * sin 51° 53" } = 23.41 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.4**2+2 * 45.8**2 - 36.4**2 } }{ 2 } = 37.149 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 45.8**2+2 * 36.4**2 - 36.4**2 } }{ 2 } = 37.149 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.4**2+2 * 36.4**2 - 45.8**2 } }{ 2 } = 28.294 ; ;
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