An aircraft is flying along a horizontal path PQ directly towards an observer on the ground at O and maintaining - Maths - Some Applications of Trigonometry

Question

An aircraft is flying along a horizontal path PQ directly towards
an observer on the ground at O and maintaining an altitude of 3000m
When the aircraft is at P, the angle of depression is 30 and when
at Q, the angle of depression is 60 Find the distance of PQ

Shruti Tyagi · Accepted Answer

Dear student,

In ∆AQBtan 60°=BQAB⇒3=3000AB⇒AB=30003 mIn ∆APCtan 30°=PCAC⇒13 =3000AC⇒AC=30003 Now, BC=AC-AB⇒BC=30003-30003⇒BC=30003-13⇒BC=30003-13⇒BC=3000×23⇒BC=60003×33⇒BC=600033⇒BC=20003 mbut from fig, PQ=BC⇒PQ=20003m⇒PQ=2000×1
73 m⇒PQ=3460 m

Regards

An aircraft is flying along a horizontal path PQ directly towards an observer on the ground at O and maintaining an altitude of 3000m. When the aircraft is at P, the angle of depression is 30 and when at Q, the angle of depression is 60. Find the distance of PQ.