Two groves

Two groves A B are separated by a forest. Both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B if AC = 5004 m, BC = 2600 m, and angle ABC = 53° 45'?

Correct answer:

c =  6080.9313 m

Step-by-step explanation:

b=5004 m a=2600 m B=53+45/60=4215=53.75   c2 =a2 +c2  2ac cos β  k=cosB=cos53.75° =0.59131  b2=a2+c22 a c k  50042=26002+c22 2600 c 0.59130964836358 c2+3074.81c+18280016=0 c23074.81c18280016=0  p=1;q=3074.81;r=18280016 D=q24pr=3074.81241(18280016)=82574521.590713 D>0  c1,2=2pq±D=23074.81±82574521.59 c1,2=1537.405086±4543.526207 c1=6080.931293184 c2=3006.121121692  c=c1=6080.9313=6080.9313 m

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