A man on the bank of the stream observes a tree on the opposition bank exactly across a stream. He finds that the angle of elevation of the top to be 45°. On reaching perpendicularly a distance of 4 m from the bank, he finds that the angle of elevation reduces by 15°. Is this information sufficient for the man to determine the height of the tree and the width of the stream? If so, find them.
Answers
Answered by
23
see diagram.
Since the angle of elevation = 45°, the width AC of the river = height CD of the tree on the other bank. Initially the man is at point A. Then he travels to the point B , AB = 4 m.
∠DBA = 45° - 15° = 30°.
Using trigonometry : DC = AC = w. as tan 45° = 1.
Tan 30° = 1/√3 = w/(w+4)
=> w + 4 = √3 w
=> w = height of tree = river width = 4/(√3 -1) = 4 * (√3+1) / 2 meters
= 2 (√3 + 1) m
We have neglected the height of the man in this calculations.
Since the angle of elevation = 45°, the width AC of the river = height CD of the tree on the other bank. Initially the man is at point A. Then he travels to the point B , AB = 4 m.
∠DBA = 45° - 15° = 30°.
Using trigonometry : DC = AC = w. as tan 45° = 1.
Tan 30° = 1/√3 = w/(w+4)
=> w + 4 = √3 w
=> w = height of tree = river width = 4/(√3 -1) = 4 * (√3+1) / 2 meters
= 2 (√3 + 1) m
We have neglected the height of the man in this calculations.
Attachments:
kvnmurty:
:-)
the ans =5.46 m in my book
you cannot even calculate 2(sqrt3 +1)
dont ask me any questions in future.
sorry sir
dont be angry
why cant you even solve it.. i mean by seeing the answer.. dont you even think how did it come
@Brainly I was a little tired at that moment so I didnt understand. ill take care from now
Nice answer sir
@Abhay Yes. A very nice answer. Answers of KVN sir are very detailed and nice
Similar questions