SOLUTION: A man finds the angle of elevation of the top of a tower to be 30o. He walks 85m nearer the tower and finds its angle of elevation to be 60o. What is the highest of the tower?

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Question 739480: A man finds the angle of elevation of the top of a tower to be 30o. He walks 85m nearer the tower and finds its angle of elevation to be 60o. What is the highest of the tower?
Answer by mananth(16946) About Me  (Show Source):
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A man finds the angle of elevation of the top of a tower to be 30o. He walks 85m nearer the tower and finds its angle of elevation to be 60o. What is the highest of the tower?
let distance from foot of tower be x
height of tower be y
theta=30
Tan 30 = y/x
y=x *tan 30
85 m closer
so distance = x-85
theta=60
tan 60 = y/(x-85)
y=(x-85)*tan60
(x-85)*tan 60 =x tan 30
xtan 60-85tan60=xtan30
xtan60-xtan30=85tan60
x(tan60-tan30)=85tan60
x=85tan60/(tan60-tan30)
x=147.22/1.154
x= 127.5
cos 30 = x/127.5
=110.4 m height of tower