7 24 25 triangle

Right scalene triangle.

Sides: a = 7   b = 24   c = 25

Area: T = 84
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 16.26602047083° = 16°15'37″ = 0.28437941092 rad
Angle ∠ B = β = 73.74397952917° = 73°44'23″ = 1.28770022176 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 24
Height: hb = 7
Height: hc = 6.72

Median: ma = 24.25438656713
Median: mb = 13.89224439894
Median: mc = 12.5

Inradius: r = 3
Circumradius: R = 12.5

Vertex coordinates: A[25; 0] B[0; 0] C[1.96; 6.72]
Centroid: CG[8.98766666667; 2.24]
Coordinates of the circumscribed circle: U[12.5; -0]
Coordinates of the inscribed circle: I[4; 3]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7439795292° = 163°44'23″ = 0.28437941092 rad
∠ B' = β' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




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 = 24 ; ; c = 25 ; ;

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

p = a+b+c = 7+24+25 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-7)(28-24)(28-25) } ; ; T = sqrt{ 7056 } = 84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84 }{ 7 } = 24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84 }{ 24 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84 }{ 25 } = 6.72 ; ;

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**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 16° 15'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 73° 44'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84 }{ 28 } = 3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 15'37" } = 12.5 ; ;




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