Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 7   b = 15   c = 15

Area: T = 51.05108325104
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 26.98767976431° = 26°59'12″ = 0.47110084734 rad
Angle ∠ B = β = 76.50766011784° = 76°30'24″ = 1.33552920901 rad
Angle ∠ C = γ = 76.50766011784° = 76°30'24″ = 1.33552920901 rad

Height: ha = 14.58659521458
Height: hb = 6.8076777668
Height: hc = 6.8076777668

Median: ma = 14.58659521458
Median: mb = 8.98661003778
Median: mc = 8.98661003778

Inradius: r = 2.765950446
Circumradius: R = 7.71329006646

Vertex coordinates: A[15; 0] B[0; 0] C[1.63333333333; 6.8076777668]
Centroid: CG[5.54444444444; 2.26989258893]
Coordinates of the circumscribed circle: U[7.5; 1.87996768218]
Coordinates of the inscribed circle: I[3.5; 2.765950446]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.0133202357° = 153°48″ = 0.47110084734 rad
∠ B' = β' = 103.4933398822° = 103°29'36″ = 1.33552920901 rad
∠ C' = γ' = 103.4933398822° = 103°29'36″ = 1.33552920901 rad

Calculate another triangle




How did we calculate this triangle?

a = 7 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 7+15+15 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-7)(18.5-15)(18.5-15) } ; ; T = sqrt{ 2606.19 } = 51.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.05 }{ 7 } = 14.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.05 }{ 15 } = 6.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.05 }{ 15 } = 6.81 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 15**2+15**2-7**2 }{ 2 * 15 * 15 } ) = 26° 59'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+15**2-15**2 }{ 2 * 7 * 15 } ) = 76° 30'24" ; ; gamma = 180° - alpha - beta = 180° - 26° 59'12" - 76° 30'24" = 76° 30'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.05 }{ 18.5 } = 2.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 26° 59'12" } = 7.71 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 15**2 - 7**2 } }{ 2 } = 14.586 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 7**2 - 15**2 } }{ 2 } = 8.986 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 7**2 - 15**2 } }{ 2 } = 8.986 ; ;
Calculate another triangle

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

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