Triangle calculator

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

You have entered perimeter p and aspect ratio a:b:c = 5:6:5.

Acute isosceles triangle.

Sides: a = 35   b = 42   c = 35

Area: T = 588
Perimeter: p = 112
Semiperimeter: s = 56

Angle ∠ A = α = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ B = β = 73.74397952917° = 73°44'23″ = 1.28770022176 rad
Angle ∠ C = γ = 53.13301023542° = 53°7'48″ = 0.9277295218 rad

Height: ha = 33.6
Height: hb = 28
Height: hc = 33.6

Median: ma = 34.47110023063
Median: mb = 28
Median: mc = 34.47110023063

Inradius: r = 10.5
Circumradius: R = 21.875

Vertex coordinates: A[35; 0] B[0; 0] C[9.8; 33.6]
Centroid: CG[14.93333333333; 11.2]
Coordinates of the circumscribed circle: U[17.5; 13.125]
Coordinates of the inscribed circle: I[14; 10.5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ B' = β' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad
∠ C' = γ' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad

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How did we calculate this triangle?

1. Input data entered: perimeter p and aspect ratio a:b:c.

p = 112 ; ; a:b:c = 5:6:5 ; ;


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 = 35 ; ; b = 42 ; ; c = 35 ; ;

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

p = a+b+c = 35+42+35 = 112 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 112 }{ 2 } = 56 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 56 * (56-35)(56-42)(56-35) } ; ; T = sqrt{ 345744 } = 588 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 588 }{ 35 } = 33.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 588 }{ 42 } = 28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 588 }{ 35 } = 33.6 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 35**2-42**2-35**2 }{ 2 * 42 * 35 } ) = 53° 7'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 42**2-35**2-35**2 }{ 2 * 35 * 35 } ) = 73° 44'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 35**2-35**2-42**2 }{ 2 * 42 * 35 } ) = 53° 7'48" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 588 }{ 56 } = 10.5 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 53° 7'48" } = 21.88 ; ;




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