SOLUTION: 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

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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 able of elevation to be 30� . Let CD is 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
Answer by ankor@dixie-net.com(22740) (Show Source):
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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 = tan(30)(x+40)
and at B
tan(60) =
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 =
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 = tan(30) * 60
h = 34.64 m is the height of the tree