SOLUTION: A railway company is building a new railroad. Surveyors wish to measure the height of a hill and the length of a tunnel to be cut through the base of the hill. At the East end of t

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Question 1154552: A railway company is building a new railroad. Surveyors wish to measure the height of a hill and the length of a tunnel to be cut through the base of the hill. At the East end of the tunnel, the surveyors measure the angle of elevation of the top of the hill to be 60°. When they move 80 metres further East, the angle of elevation to the top of the hill is 45°. From a point 120 metres to the West of the West end of the tunnel, the angle of elevation of the top of the hill is 30°. Find the length of the tunnel l.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

TAN (45) =MC /CE
MC = CE ( tan 45 =1)
tan 60 = MC/CD
sqrt%283%29 = MC/CD
= CE/CD
.
CD = CE/ sqrt(3)
sqrt(3) *CD = CE
1.73CD= CD+DE
0.73CD =80
tan 30 = 1/sqrt(3) =MC/AC
AC = MC * sqrt(3)
= 189.6*1.73
=328
BC = 328-120 =208
Length of tunnel =208 +110=318 m