Vidhyamath Forum

Height and Distance

Rita Lamichhane

Student

A man 1.5m tall standing at a distance of 50m from a tree observes the angle of elevation of the top of the tree is 45°. Find the height of the tree.

24 Dec, 2023

Replies (3)

Apozee Online Academy

Instructor

Let CE be the height of the tree, AB be the height of the man and BC is the distance between the foot of the tree and the man.

Here,

AB = 1.5m

BC = 50m

Angle of elevation, ∠DAE = 45°

In rectangle ABCD,

DC = AB = 1.5m

AD = BC = 50m

In right angled triangle ADE,

tan45° = p/b = ED/AD = ED/50

or, 1 = ED/50

or, ED = 50m

Now, CE = ED + DC

= 50 + 1.5

= 51.5m

So, the required height of the tree is 51.5m.

24 Dec, 2023

Rita Lamichhane

Student

Thank you sir

25 Dec, 2023

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