Suppose angle of depression from top of the tower to point A is 45°. And height of tower is 10 m. What is the distance of point A from the building?

How to find Distance when angle of depression is given 1.jpg

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Let building be BC

 

So, angle of depression from point B is 45°

and Height = BC = 10 m

BX is the horizontal

 

Now, we need to find the distance of point A from the building

 

Now, lines BX and AC are parallel,

and AB is the transversal

So, Alternate angles are equal

∴ ∠ BAC = ∠ XBA

∴ ∠ BAC = 45°

How to find Distance when angle of depression is given? - Part 2

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Now, we need to find base AC

And we are given height 10 m.

 

So, we can use tan

As

tan A = Side opposite to angle A / Side adjacent to angle A

tan 45° = BC / AC

1 = 10/ AC

AC = 10 m

 

∴ Distance AC is 10 m

  1. Chapter 9 Class 10 Some Applications of Trigonometry (Term 2)
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.