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=2154=53.75  c2=a2+c22accosβ  k=cosB=cos53.75 =0.59131  b2=a2+c22ack  50042=26002+c22 2600 c 0.591309648364 c2+3074.81c+18280016=0 c23074.81c18280016=0  p=1;q=3074.81;r=18280016 D=q24pr=3074.81241(18280016)=82574521.5907 D>0  c1,2=q±D2p=3074.81±82574521.592 c1,2=1537.40508575±4543.52620744 c1=6080.93129318 c2=3006.12112169   Factored form of the equation:  (c6080.93129318)(c+3006.12112169)=0  c=c1=6080.9313 m

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