Question:
The angles of depression of two consecutive kilometre stones on the road on right and left of an aeroplane are 60° and 45°,respetively as observed from the aeroplane.Find the height of the aeroplane
Answer:
Let height of the aeroplane is h
Let two stones are at A and C and distance between two stones is 1 km.
Again from triangle AOB,
tan 45 = OB/OA
=> 1 = h/OA
=> OA = h
Now from triangle COB,
tan 60 = OB/OC
=> √3 = h/(AC - OA)
=> √3 = h/(1 - h)
=> √3(1 - h) = h
=> √3 - √3h = h
=> √3h + h = √3
=> (√3 + 1)h = √3
=> h = √3/(√3 + 1)
=> h = {√3*(√3 - 1)}/{(√3 + 1)*(√3 - 1)}
=> h = {√3*(√3 - 1)}/(3 - 1)
=> h = √3*(√3 - 1)/2
=> h = (3 - √3)/2 km
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