The farmer

The farmer sees the back fence of the land, which is 50 m long at a viewing angle of 30 degrees. It is 92 m away from one end of the fence. How far is it from the other end of the fence?

Correct answer:

c1 =  99.2703 m
c2 =  60.0784 m

Step-by-step explanation:

a=50 m α=30 ° b=92 m  a2=b2+c22 b c cosα  k=2 b cosα°=2 b cos30° =2 92 cos30° =2 92 0.866025=159.34867 m  a2=b2+c2kc  502=922+c2159.348674296 c c2+159.349c5964=0 c2159.349c+5964=0  p=1;q=159.349;r=5964 D=q24pr=159.3492415964=1535.99999989 D>0  c1,2=q±D2p=159.35±15362 c1,2=79.67433715±19.5959179416 c1=99.2702550896=99.2703 m c2=60.0784192064   Factored form of the equation:  (c99.2702550896)(c60.0784192064)=0

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