How to find Distance when angle of depression is given?

Last updated at April 16, 2024 by

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

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

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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.