Height and Distance
Rita Lamichhane
Student
- 2
- 392
- 3
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)
Vidhyamath Online
Instructor
- 45
- 1
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
- 2
Thank you sir
- 25 Dec, 2023
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