Magnitudes 64704

The triangle ABC determines the size of the sides a and b and the magnitudes of the interior angles β and γ, given c = 1.86 m, the line on the side c is 2.12 m, and the angle alpha is 40 ° 12 '.

Correct answer:

a =  1.7865 m
b =  2.7436 m
β =  97.576 °
γ =  42.224 °

Step-by-step explanation:

c=1.86 m m3=2.12 m α=40+12/60=5201=40.2   m32 = (c/2)2 + b2  2(c/2) b  cos α  k1=cos(α)=cos(40.2°)0.7638  m32=(c/2)2+b22 (c/2) b k1  2.122=(1.86/2)2+b22 (1.86/2) b 0.76379602863464 b2+1.421b+3.63=0 b21.421b3.63=0  p=1;q=1.421;r=3.63 D=q24pr=1.421241(3.63)=16.5362765781 D>0  b1,2=2pq±D=21.42±16.54 b1,2=0.71033±2.033241 b1=2.743571351 b2=1.322910738 b=b1=2.74362.7436  a2 = b2+c2  2 b c  cos α  a=b2+c22 b c cosα=b2+c22 b c cos40.2° =2.74362+1.8622 2.7436 1.86 cos40.2° =2.74362+1.8622 2.7436 1.86 0.763796=1.786=1.7865 m

Our quadratic equation calculator calculates it.

β=π180°arccos(2 a ca2+c2b2)=π180°arccos(2 1.7865 1.861.78652+1.8622.74362)=97.576=97°3434"

Try calculation via our triangle calculator.

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