Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 14   b = 20   c = 20

Area: T = 131.1454957966
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 40.97546302294° = 40°58'29″ = 0.71551422073 rad
Angle ∠ B = β = 69.51326848853° = 69°30'46″ = 1.21332252231 rad
Angle ∠ C = γ = 69.51326848853° = 69°30'46″ = 1.21332252231 rad

Height: ha = 18.73549939952
Height: hb = 13.11444957966
Height: hc = 13.11444957966

Median: ma = 18.73549939952
Median: mb = 14.07112472795
Median: mc = 14.07112472795

Inradius: r = 4.85772206654
Circumradius: R = 10.67552102537

Vertex coordinates: A[20; 0] B[0; 0] C[4.9; 13.11444957966]
Centroid: CG[8.3; 4.37114985989]
Coordinates of the circumscribed circle: U[10; 3.73663235888]
Coordinates of the inscribed circle: I[7; 4.85772206654]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0255369771° = 139°1'31″ = 0.71551422073 rad
∠ B' = β' = 110.4877315115° = 110°29'14″ = 1.21332252231 rad
∠ C' = γ' = 110.4877315115° = 110°29'14″ = 1.21332252231 rad

Calculate another triangle




How did we calculate this triangle?

a = 14 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 14+20+20 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-14)(27-20)(27-20) } ; ; T = sqrt{ 17199 } = 131.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.14 }{ 14 } = 18.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.14 }{ 20 } = 13.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.14 }{ 20 } = 13.11 ; ;

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{ 20**2+20**2-14**2 }{ 2 * 20 * 20 } ) = 40° 58'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+20**2-20**2 }{ 2 * 14 * 20 } ) = 69° 30'46" ; ; gamma = 180° - alpha - beta = 180° - 40° 58'29" - 69° 30'46" = 69° 30'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.14 }{ 27 } = 4.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 40° 58'29" } = 10.68 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 20**2 - 14**2 } }{ 2 } = 18.735 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 14**2 - 20**2 } }{ 2 } = 14.071 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 14**2 - 20**2 } }{ 2 } = 14.071 ; ;
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.