Triangle calculator - result

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, angle α and angle γ.

Obtuse scalene triangle.

Sides: a = 10   b = 15.2498529258   c = 7.64327677116

Area: T = 33.42325762884
Perimeter: p = 32.89112969696
Semiperimeter: s = 16.44656484848

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 119° = 2.07769418099 rad
Angle ∠ C = γ = 26° = 0.45437856055 rad

Height: ha = 6.68545152577
Height: hb = 4.38437114679
Height: hc = 8.74661970714

Median: ma = 10.97656444646
Median: mb = 4.59109190816
Median: mc = 12.31548628775

Inradius: r = 2.03223051608
Circumradius: R = 8.71772339781

Vertex coordinates: A[7.64327677116; 0] B[0; 0] C[-4.84880962025; 8.74661970714]
Centroid: CG[0.93215571697; 2.91553990238]
Coordinates of the circumscribed circle: U[3.82113838558; 7.83549979997]
Coordinates of the inscribed circle: I[1.19771192268; 2.03223051608]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 61° = 2.07769418099 rad
∠ C' = γ' = 154° = 0.45437856055 rad

Calculate another triangle


How did we calculate this triangle?

1. Input data entered: side a, angle α and angle γ.

a = 10 ; ; alpha = 35° ; ; gamma = 26° ; ;

2. From angle α and angle γ we calculate angle β:

 alpha + gamma + beta = 180° ; ; beta = 180° - alpha - gamma = 180° - 35 ° - 26 ° = 119 ° ; ;

3. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b:

 fraction{ b }{ a } = fraction{ sin beta }{ sin alpha } ; ; ; ; b = a * fraction{ sin beta }{ sin alpha } ; ; ; ; b = 10 * fraction{ sin 119° }{ sin 35° } = 15.25 ; ;

4. From angle γ, angle α and side a we calculate side c - By using the law of sines, we calculate unknown side c:

 fraction{ c }{ a } = fraction{ sin gamma }{ sin alpha } ; ; ; ; c = a * fraction{ sin gamma }{ sin alpha } ; ; ; ; c = 10 * fraction{ sin 26° }{ sin 35° } = 7.64 ; ;
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 = 10 ; ; b = 15.25 ; ; c = 7.64 ; ;

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

p = a+b+c = 10+15.25+7.64 = 32.89 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.89 }{ 2 } = 16.45 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.45 * (16.45-10)(16.45-15.25)(16.45-7.64) } ; ; T = sqrt{ 1117.07 } = 33.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.42 }{ 10 } = 6.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.42 }{ 15.25 } = 4.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.42 }{ 7.64 } = 8.75 ; ;

9. 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{ 15.25**2+7.64**2-10**2 }{ 2 * 15.25 * 7.64 } ) = 35° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+7.64**2-15.25**2 }{ 2 * 10 * 7.64 } ) = 119° ; ;
 gamma = 180° - alpha - beta = 180° - 35° - 119° = 26° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.42 }{ 16.45 } = 2.03 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 35° } = 8.72 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 7.64**2 - 10**2 } }{ 2 } = 10.976 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.64**2+2 * 10**2 - 15.25**2 } }{ 2 } = 4.591 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 10**2 - 7.64**2 } }{ 2 } = 12.315 ; ;
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.