Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 69.06   b = 84.11   c = 48

Area: T = 1657.443997246
Perimeter: p = 201.17
Semiperimeter: s = 100.585

Angle ∠ A = α = 55.19218114379° = 55°11'31″ = 0.96332788297 rad
Angle ∠ B = β = 90.01104441111° = 90°38″ = 1.57109786109 rad
Angle ∠ C = γ = 34.7987744451° = 34°47'52″ = 0.60773352129 rad

Height: ha = 487.9999992025
Height: hb = 39.41112465215
Height: hc = 69.06599988527

Median: ma = 59.13548048953
Median: mb = 42.04878153416
Median: mc = 73.11655787093

Inradius: r = 16.47880034047
Circumradius: R = 42.05550006987

Vertex coordinates: A[48; 0] B[0; 0] C[-0.01325885417; 69.06599988527]
Centroid: CG[15.99658038194; 23.02199996176]
Coordinates of the circumscribed circle: U[24; 34.53443753927]
Coordinates of the inscribed circle: I[16.475; 16.47880034047]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8088188562° = 124°48'29″ = 0.96332788297 rad
∠ B' = β' = 89.99895558889° = 89°59'22″ = 1.57109786109 rad
∠ C' = γ' = 145.2022255549° = 145°12'8″ = 0.60773352129 rad

Calculate another triangle




How did we calculate this triangle?

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

p = a+b+c = 69.06+84.11+48 = 201.17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 201.17 }{ 2 } = 100.59 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 100.59 * (100.59-69.06)(100.59-84.11)(100.59-48) } ; ; T = sqrt{ 2747107.26 } = 1657.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1657.44 }{ 69.06 } = 48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1657.44 }{ 84.11 } = 39.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1657.44 }{ 48 } = 69.06 ; ;

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{ 84.11**2+48**2-69.06**2 }{ 2 * 84.11 * 48 } ) = 55° 11'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 69.06**2+48**2-84.11**2 }{ 2 * 69.06 * 48 } ) = 90° 38" ; ; gamma = 180° - alpha - beta = 180° - 55° 11'31" - 90° 38" = 34° 47'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1657.44 }{ 100.59 } = 16.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 69.06 }{ 2 * sin 55° 11'31" } = 42.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 84.11**2+2 * 48**2 - 69.06**2 } }{ 2 } = 59.135 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 69.06**2 - 84.11**2 } }{ 2 } = 42.048 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 84.11**2+2 * 69.06**2 - 48**2 } }{ 2 } = 73.116 ; ;
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.