Triangle calculator

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

You have entered side a, angle β and angle γ.

Acute scalene triangle.

Sides: a = 17.5   b = 17.5   c = 9.05986665786

Area: T = 76.56325
Perimeter: p = 44.05986665786
Semiperimeter: s = 22.02993332893

Angle ∠ A = α = 75° = 1.3098996939 rad
Angle ∠ B = β = 75° = 1.3098996939 rad
Angle ∠ C = γ = 30° = 0.52435987756 rad

Height: ha = 8.75
Height: hb = 8.75
Height: hc = 16.90437019601

Median: ma = 10.84439946556
Median: mb = 10.84439946556
Median: mc = 16.90437019601

Inradius: r = 3.47554796704
Circumradius: R = 9.05986665786

Vertex coordinates: A[9.05986665786; 0] B[0; 0] C[4.52993332893; 16.90437019601]
Centroid: CG[4.52993332893; 5.635456732]
Coordinates of the circumscribed circle: U[4.52993332893; 7.84550353815]
Coordinates of the inscribed circle: I[4.52993332893; 3.47554796704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105° = 1.3098996939 rad
∠ B' = β' = 105° = 1.3098996939 rad
∠ C' = γ' = 150° = 0.52435987756 rad

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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 = 17.5 ; ; b = 17.5 ; ; c = 9.06 ; ;

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

p = a+b+c = 17.5+17.5+9.06 = 44.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.06 }{ 2 } = 22.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.03 * (22.03-17.5)(22.03-17.5)(22.03-9.06) } ; ; T = sqrt{ 5861.82 } = 76.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.56 }{ 17.5 } = 8.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.56 }{ 17.5 } = 8.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.56 }{ 9.06 } = 16.9 ; ;

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{ 17.5**2-17.5**2-9.06**2 }{ 2 * 17.5 * 9.06 } ) = 75° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17.5**2-17.5**2-9.06**2 }{ 2 * 17.5 * 9.06 } ) = 75° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.06**2-17.5**2-17.5**2 }{ 2 * 17.5 * 17.5 } ) = 30° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.56 }{ 22.03 } = 3.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.5 }{ 2 * sin 75° } = 9.06 ; ;




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