7 7 8 triangle

Acute isosceles triangle.

Sides: a = 7   b = 7   c = 8

Area: T = 22.97882505862
Perimeter: p = 22
Semiperimeter: s = 11

Angle ∠ A = α = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ B = β = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ C = γ = 69.76998091581° = 69°41'59″ = 1.21664911578 rad

Height: ha = 6.56552144532
Height: hb = 6.56552144532
Height: hc = 5.74545626465

Median: ma = 6.65220673478
Median: mb = 6.65220673478
Median: mc = 5.74545626465

Inradius: r = 2.08989318715
Circumradius: R = 4.26549025709

Vertex coordinates: A[8; 0] B[0; 0] C[4; 5.74545626465]
Centroid: CG[4; 1.91548542155]
Coordinates of the circumscribed circle: U[4; 1.48796600756]
Coordinates of the inscribed circle: I[4; 2.08989318715]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ B' = β' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ C' = γ' = 110.3300190842° = 110°18'1″ = 1.21664911578 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 7 ; ; b = 7 ; ; c = 8 ; ;

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

p = a+b+c = 7+7+8 = 22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22 }{ 2 } = 11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11 * (11-7)(11-7)(11-8) } ; ; T = sqrt{ 528 } = 22.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.98 }{ 7 } = 6.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.98 }{ 7 } = 6.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.98 }{ 8 } = 5.74 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 7**2-7**2-8**2 }{ 2 * 7 * 8 } ) = 55° 9' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-7**2-8**2 }{ 2 * 7 * 8 } ) = 55° 9' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 69° 41'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.98 }{ 11 } = 2.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 55° 9' } = 4.26 ; ;




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