Triangle calculator

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

You have entered side a, b and angle γ.

Acute isosceles triangle.

Sides: a = 1.5   b = 1.5   c = 1.92883628291

Area: T = 1.10879087221
Perimeter: p = 4.92883628291
Semiperimeter: s = 2.46441814145

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 50° = 0.8732664626 rad
Angle ∠ C = γ = 80° = 1.39662634016 rad

Height: ha = 1.47772116295
Height: hb = 1.47772116295
Height: hc = 1.14990666647

Median: ma = 1.55662106542
Median: mb = 1.55662106542
Median: mc = 1.14990666647

Inradius: r = 0.45496051774
Circumradius: R = 0.9799055467

Vertex coordinates: A[1.92883628291; 0] B[0; 0] C[0.96441814145; 1.14990666647]
Centroid: CG[0.96441814145; 0.38330222216]
Coordinates of the circumscribed circle: U[0.96441814145; 0.17700111977]
Coordinates of the inscribed circle: I[0.96441814145; 0.45496051774]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 130° = 0.8732664626 rad
∠ C' = γ' = 100° = 1.39662634016 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 = 1.5 ; ; b = 1.5 ; ; c = 1.93 ; ;

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

p = a+b+c = 1.5+1.5+1.93 = 4.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4.93 }{ 2 } = 2.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.46 * (2.46-1.5)(2.46-1.5)(2.46-1.93) } ; ; T = sqrt{ 1.23 } = 1.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.11 }{ 1.5 } = 1.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.11 }{ 1.5 } = 1.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.11 }{ 1.93 } = 1.15 ; ;

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{ 1.5**2-1.5**2-1.93**2 }{ 2 * 1.5 * 1.93 } ) = 50° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.5**2-1.5**2-1.93**2 }{ 2 * 1.5 * 1.93 } ) = 50° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.93**2-1.5**2-1.5**2 }{ 2 * 1.5 * 1.5 } ) = 80° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.11 }{ 2.46 } = 0.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.5 }{ 2 * sin 50° } = 0.98 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.