From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30^ and 45^ . The height of the aeroplane above the ground is:

Step-by-step solution

array ll In ABD , & 45^ = h x & 1= h x h=x array In ABC , array rlrl & & 30^ & = h x+20 & 1 3 & = h x+20 = h h+20 ( x=h) & 3 h & =h+20=( 3 h-h)=20 & h( 3 -1) & =20 & h & = 20 3 -1 3 +1 3 +1 = 20( 3 +1) 2 & h & =10( 3 +1) array Hence, height of the aeroplane above the ground =10( 3 +1) m .