A pilot is traveling at a height of 30,000 feet above ground she looks down at a angle of depression of 6 and spots runway as measured along the ground how many miles away is she from the runway

Distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.Solution:Given that Height of position of pilot from the ground = 30000 feet Angle of depression when he looks down at runway = 6o Need to measure along the ground, distance between runway and pilot that is horizontal distance between runway and pilot. Consider the figure attached belowD represents position of runway.  P represents position of pilot. PG represents height of position of pilot from the ground that means PG = 30000 feet PH is virtual horizontal line and HPD is angle of depression means ∠ HPD = 6 degreeAS DG and HP are horizontals, so DG is parallel to HP. =>  ∠ HPD =∠ PDG =  6 degree  [ Alternate interior angle made by transversal PD of two parallel lines ] We need to calculate DG Consider right angles triangle PGD right angles at G [tex]\text {As } \tan x=\frac{\text { Perpendicular }}{\text { Base }}[/tex][tex]\tan \angle \mathrm{PDG}=\frac{\mathrm{PG}}{\mathrm{GD}}[/tex][tex]\begin{array}{l}{=>\mathrm{GD}=\frac{\mathrm{PG}}{\tan \angle \mathrm{PDG}}} \\\\ {=>\mathrm{GD}=\frac{30000}{\tan 6^{\circ}}=285430.9336}\end{array}[/tex]As one foot = 0.000189 miles[tex]=>285430.9336 \text { feet }=285430.9336 \times 0.000189 \text { miles }=53.9464 \text { miles. }[/tex]Hence distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.