4 6 7 triangle

Acute scalene triangle.

Sides: a = 4   b = 6   c = 7

Area: T = 11.9776539567
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ B = β = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ C = γ = 86.41766783015° = 86°25' = 1.5088255565 rad

Height: ha = 5.98882697835
Height: hb = 3.99221798557
Height: hc = 3.42218684477

Median: ma = 6.2054836823
Median: mb = 4.84876798574
Median: mc = 3.70880992435

Inradius: r = 1.40990046549
Circumradius: R = 3.50768560301

Vertex coordinates: A[7; 0] B[0; 0] C[2.07114285714; 3.42218684477]
Centroid: CG[3.02438095238; 1.14106228159]
Coordinates of the circumscribed circle: U[3.5; 0.21991785019]
Coordinates of the inscribed circle: I[2.5; 1.40990046549]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ B' = β' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ C' = γ' = 93.58333216985° = 93°35' = 1.5088255565 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 = 4 ; ; b = 6 ; ; c = 7 ; ;

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

p = a+b+c = 4+6+7 = 17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17 }{ 2 } = 8.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.5 * (8.5-4)(8.5-6)(8.5-7) } ; ; T = sqrt{ 143.44 } = 11.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.98 }{ 4 } = 5.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.98 }{ 6 } = 3.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.98 }{ 7 } = 3.42 ; ;

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{ 4**2-6**2-7**2 }{ 2 * 6 * 7 } ) = 34° 46'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-4**2-7**2 }{ 2 * 4 * 7 } ) = 58° 48'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-4**2-6**2 }{ 2 * 6 * 4 } ) = 86° 25' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.98 }{ 8.5 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 34° 46'19" } = 3.51 ; ;




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

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