Answer:
The distance of the plane from the base of the tower is 25.5 foot.
Step-by-step explanation:
As given
Max is in a control tower at a small airport.
He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27°.
Now by using the trigonometric identity.
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
As shown in the figure given below
Perpendicular = CB
Base = AC = 50 feet
[tex]\theta = 27^{\circ}[/tex]
Put in the identity.
[tex]tan\ 27^{\circ} = \frac{CB}{AC}[/tex]
[tex]tan\ 27^{\circ} = \frac{CB}{50}[/tex]
[tex]tan\ 27^{\circ} = 0.51\ (Approx)[/tex]
Put in the above
[tex]0.51 = \frac{CB}{50}[/tex]
CB = 0.51 × 50
CB = 25.5 foot
Therefore the distance of the plane from the base of the tower is 25.5 foot.
