An airplane is flying at an altitude of approximately 2 miles above ground level. The pilot sights a landmark at an angle of depression of 11°. One minute later, the pilot sights the same landmark at an angle of depression of 18°. To the nearest tenth of a mile, how far did the plane fly in that minute?

0.3 miles

Step-by-step explanation:

Using Trigonometry ;

Height, h = 2 miles

First sighting :  

Horizontal distance h1 ;

h1 = 2tanθ

θ = 11°

h1 = 2 * 0.1943803

h1 = 0.3887606 miles

Second sighting ;

Horizontal distance h2 ;

h2 = 2tanθ

θ = 18°

h2 = 2 * 0.3249196

h2 = 0.6498393 miles

Horizontal difference :

0.6498393 miles - 0.3887606 miles

= 0.2610787 miles

= 0.3 miles

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(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47