79.37 79.37 112.25 triangle

Obtuse isosceles triangle.

Sides: a = 79.37   b = 79.37   c = 112.25

Area: T = 3149.798844251
Perimeter: p = 270.99
Semiperimeter: s = 135.495

Angle ∠ A = α = 44.99880247608° = 44°59'53″ = 0.7855363689 rad
Angle ∠ B = β = 44.99880247608° = 44°59'53″ = 0.7855363689 rad
Angle ∠ C = γ = 90.00439504785° = 90°14″ = 1.57108652757 rad

Height: ha = 79.37699998113
Height: hb = 79.37699998113
Height: hc = 56.12111303789

Median: ma = 88.74108050166
Median: mb = 88.74108050166
Median: mc = 56.12111303789

Inradius: r = 23.24766027714
Circumradius: R = 56.12550001334

Vertex coordinates: A[112.25; 0] B[0; 0] C[56.125; 56.12111303789]
Centroid: CG[56.125; 18.70770434596]
Coordinates of the circumscribed circle: U[56.125; -0.00438697546]
Coordinates of the inscribed circle: I[56.125; 23.24766027714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0021975239° = 135°7″ = 0.7855363689 rad
∠ B' = β' = 135.0021975239° = 135°7″ = 0.7855363689 rad
∠ C' = γ' = 89.99660495215° = 89°59'46″ = 1.57108652757 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 = 79.37+79.37+112.25 = 270.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 270.99 }{ 2 } = 135.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 135.5 * (135.5-79.37)(135.5-79.37)(135.5-112.25) } ; ; T = sqrt{ 9921230.23 } = 3149.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3149.8 }{ 79.37 } = 79.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3149.8 }{ 79.37 } = 79.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3149.8 }{ 112.25 } = 56.12 ; ;

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{ 79.37**2+112.25**2-79.37**2 }{ 2 * 79.37 * 112.25 } ) = 44° 59'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 79.37**2+112.25**2-79.37**2 }{ 2 * 79.37 * 112.25 } ) = 44° 59'53" ; ;
 gamma = 180° - alpha - beta = 180° - 44° 59'53" - 44° 59'53" = 90° 14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3149.8 }{ 135.5 } = 23.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 79.37 }{ 2 * sin 44° 59'53" } = 56.13 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 79.37**2+2 * 112.25**2 - 79.37**2 } }{ 2 } = 88.741 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 112.25**2+2 * 79.37**2 - 79.37**2 } }{ 2 } = 88.741 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 79.37**2+2 * 79.37**2 - 112.25**2 } }{ 2 } = 56.121 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.