the height of a hill is 270 m above the level of a horizontal plane From a point - Maths - Some Applications of Trigonometry

Question

the height of a hill is 270 m above the level of a horizontal plane
From a point A on this plane the angular elevation of the top of
the hill is 60 degrees A Balloon rises from A and ascends
vertically upwards at a uniform rate; after 2 5 minutes the
angularelevationof the top of the hill to an observer in the
balloon is 30 degrees Find the speed of the balloon's ascent in m/s

Ashwini Kumar · Accepted Answer

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Let CD be the hill
∴CD=270 m⇒∠ACD=60°In △ACD,tan∠ACD=CDAC⇒tan60°=270AC⇒3=270AC⇒AC=2703=903 m⇒BE=903 mIn △DEB,tan∠EBD=DEBE⇒tan30°=DE903⇒13=DE903⇒DE=90 mNow,AB=CE=CD-ED=270-90=180 mHere, baloon takes 2
5 min to reach point B from AAnd 2
5 min = 2
5×60=150 secSpeed of baloon ascent=180150=65=1
2 m/s