Calculate 82696

In the triangle ABC, b=5 cm, c=6 cm, /BAC/ = 80° are given. Calculate the sizes of the other sides and angles, and further determine the sizes of the tangent tc and the area of the triangle.

Correct answer:

a =  7.112 cm
β =  43.8166 °
γ =  56.1834 °
t =  5.3657 cm
S =  14.7721 cm2

Step-by-step explanation:

b=5 cm c=6 cm α=80   a2 = b2+c22 b c cos α  a=b2+c22 b c cosα=b2+c22 b c cos80° =52+622 5 6 cos80° =52+622 5 6 0.173648=7.112=7.112 cm
b2 = a2+c22 a c cos β B=arccos(2 a ca2+c2b2)=arccos(2 7.112 67.1122+6252)0.7647 rad  β=B  °=B π180   °=0.7647 π180   °=43.817  °=43.8166=43°49

Try calculation via our triangle calculator.

t2 = b2+(c/2)22 b (c/2) cos α)  t=b2+(c/2)2b c cosα=b2+(c/2)2b c cos80° =52+(6/2)25 6 cos80° =52+(6/2)25 6 0.173648=5.366=5.3657 cm
s=2a+b+c=27.112+5+69.056 cm  S=s (sa) (sb) (sc)=9.056 (9.0567.112) (9.0565) (9.0566)=14.7721 cm2

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