Question 1122873
A person standing on the bank of a river observers that the angle of elevation of the top of a tree on opposite bank is 60° .
 When he was 40m away from the bank, he finds that the angle of elevation to be 30° .
 Let CD = the tree , BC is the river and the observer is standing at A. 
a) Illustrate the diagram represent the information given. 
b) Find the height of the tree, h and the width of the river, x 
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D
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h
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C-----x-------\B---40-----\A
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AC = (x+40)
Find x
tan(30) = {{{h/((x+40))}}}
h = tan(30)(x+40)
and at B
tan(60) = {{{h/x}}}
tan(60)(x) = h
h=h therfore
tan(60)x = tan(30)(x+40)
1.732x = .577(x+40)
1.732x = .577x + 23.094
1.732x - .577x = 23.094
1.155x = 23.094
x = {{{23.094/1.155}}}
x ~ 20 meters is the width of the river
Find h
Observer at A is 60 m from the base of the tree
tan(30) = {{{h/60}}}
h = tan(30) * 60
h = 34.64 m is the height of the tree