Viewing angle

The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure.
How far is the observer from the other end of the enclosure?

Correct result:

c1 =  119.9416 m
c2 =  56.7276 m

Solution:

a=60 m A=30 b=102 m  a2=b2+c22 b c cos(A)  k=2 b cosA=2 b cos30 =2 102 cos30 =2 102 0.866025=176.66918 m  a2=b2+c2kc  602=1022+c2176.669182372 c c2+176.669c6804=0 c2176.669c+6804=0  p=1;q=176.669;r=6804 D=q24pr=176.6692416804=3995.99999999 D>0  c1,2=q±D2p=176.67±39962 c1,2=88.33459119±31.6069612585 c1=119.941552445=119.9416 m c2=56.7276299275   Factored form of the equation:  (c119.941552445)(c56.7276299275)=0

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