Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 75   b = 75   c = 106.07

Area: T = 2812.549999207
Perimeter: p = 256.07
Semiperimeter: s = 128.035

Angle ∠ A = α = 44.99878484798° = 44°59'52″ = 0.78553606123 rad
Angle ∠ B = β = 44.99878484798° = 44°59'52″ = 0.78553606123 rad
Angle ∠ C = γ = 90.00443030404° = 90°15″ = 1.5710871429 rad

Height: ha = 754.9999997885
Height: hb = 754.9999997885
Height: hc = 53.03110171032

Median: ma = 83.85550681235
Median: mb = 83.85550681235
Median: mc = 53.03110171032

Inradius: r = 21.96766496823
Circumradius: R = 53.03550001496

Vertex coordinates: A[106.07; 0] B[0; 0] C[53.035; 53.03110171032]
Centroid: CG[53.035; 17.67770057011]
Coordinates of the circumscribed circle: U[53.035; -0.00439830464]
Coordinates of the inscribed circle: I[53.035; 21.96766496823]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.002215152° = 135°8″ = 0.78553606123 rad
∠ B' = β' = 135.002215152° = 135°8″ = 0.78553606123 rad
∠ C' = γ' = 89.99656969596° = 89°59'45″ = 1.5710871429 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 = 75+75+106.07 = 256.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 256.07 }{ 2 } = 128.04 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 128.04 * (128.04-75)(128.04-75)(128.04-106.07) } ; ; T = sqrt{ 7910156.21 } = 2812.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2812.5 }{ 75 } = 75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2812.5 }{ 75 } = 75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2812.5 }{ 106.07 } = 53.03 ; ;

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{ 75**2+106.07**2-75**2 }{ 2 * 75 * 106.07 } ) = 44° 59'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 75**2+106.07**2-75**2 }{ 2 * 75 * 106.07 } ) = 44° 59'52" ; ; gamma = 180° - alpha - beta = 180° - 44° 59'52" - 44° 59'52" = 90° 15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2812.5 }{ 128.04 } = 21.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 75 }{ 2 * sin 44° 59'52" } = 53.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 75**2+2 * 106.07**2 - 75**2 } }{ 2 } = 83.855 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 106.07**2+2 * 75**2 - 75**2 } }{ 2 } = 83.855 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 75**2+2 * 75**2 - 106.07**2 } }{ 2 } = 53.031 ; ;
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.