A pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is 78 degrees, and the angle of depression to the second airport is 19 degrees. What is the distance between the two airports?

the image of (6, 9) under a dilation is (4, 6). the scale factor is

12.5 feet

step-by-step explanation:

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

irrational, cannot