SOLUTION: From a certain point you observe that the top of a cliff has an angle of elevation of 45deg. If you move 60 metres directly away from the cliff along the horizontal ground, the ang

Algebra ->  Trigonometry-basics -> SOLUTION: From a certain point you observe that the top of a cliff has an angle of elevation of 45deg. If you move 60 metres directly away from the cliff along the horizontal ground, the ang      Log On


   

Question 560303: From a certain point you observe that the top of a cliff has an angle of elevation of 45deg. If you move 60 metres directly away from the cliff along the horizontal ground, the angle of elevation is now observed to be 30deg. how high is the cliff?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
first observation

45 deg
let distance from clif be x
Tan theta = opposite side / afjacent side
tan 45 = h/x
x tan 45 = h
similarly
second obsevation
(x+60)*tan 30 =h
tan30*(x+60)=x * tan 45
x tan 30+ 60 tan 60 = x *tan 45
x tan 30 -xtan 45 = -60 * tan 60

x(tan 30-Tan 45)=-60*tan 30
x=-60*tan 30/(tan 30-Tan 45)
x=-34.64/-0.422
x=82
tan 45 = h/82
82*tan 45 = h
height of cliff = 82m