A 1.5 Meters tall person is standing in front of a 41.5m high tree. When observing the top of the tree an angle of 45° is formed with the eyes. Find the distance between the tree and the person.

Aakash Shah

3 years ago

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Aakash Shah

3 years ago

Let, AB be the height of a man, CD be the height of a tree,

AE = BD be the distance between the man and the tree,

and CAE is the angle of elevation of the top of the tree.

Then, by the question

ED = AB = 1.5m

CD = 41.5m, CAE = 45° ,BD = ?

Here, CE = CD - ED = 41.5m - 1.5m = 40m

In right angled triangle CEA

Tan 45° = \(\frac{CE}{AE}\)

or, 1 = \(\frac{40m}{BD}\)

or, BD = 40m

Therefore, the distance between the man and the tree (BD) = 40m

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