The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of…

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.

Solution

x=80cos30°=403

y=80sin30°=40

tan45°=1

⇒  x+z=h

⇒  403+z=h  

tan75°=h-yz

⇒  2+3=h-40z

⇒  z=h-402+3

⇒  h-403=h-402+3

(1+3)h=80(1+3)

h=80

Asked in: JEE Main 2020 (06 Sep Shift 1)

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