1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp-post CD are observed to be 30∘ and 60∘ respectively. Find (i) the horizontal distance between AB and CD, (ii) the height of the lamp-post, (iii) the difference between the heights of the building and the lamp-post.

Open in App
Solution

## Let AB be the building of height 60m and CD be the lamp post of height h, an angle of depression of the top and bottom of vertical lamp post is 30o and 60o respectively. Let AE = h, AC = x and AC = ED It is also given AB = 60 m, Then BE = 60-h and ∠ACB=60o,∠BDE=30o (i) So we use trigonometric ratios, In right △ABC,⇒tan 60o=ABAC⇒√3=60x⇒x=60√3⇒x=34.64 m Hence distance between AB and CD is 34.64 m (ii) So again in right △BDE,⇒tan 30o=BEDE⇒1√3=60−hx⇒x=(60−h)√3⇒60√3=(60−h)√3⇒60=180−3h⇒3h=180−60⇒3h=120⇒h=40 m Hence height of the lamp post is 40 m (iii) Since BE=60−h⇒BE=60−40⇒BE=20 Hence the difference between the height of building and lamp post is 20 m

Suggest Corrections
104
Join BYJU'S Learning Program
Related Videos
Angle of depression_tackle
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program