suppose that you see a flock of birds at an angle of elevation pf 32 degrees. If the birds are at an altitude of 12,000 feet, and if your eye level is 6 feet above the ground, then what is your horizontal distance from the birds?

Accepted Solution

You can draw a right triangle between you and the flock of birds using your horizontal line of sight, the elevation angle, and the altitude of the birds.
Notice that in your triangle, the opposite side of your elevation angle will be the altitude of the flock of birds minus your eye level above the ground:
[tex]12000-6=11994[/tex] feet 
Also, the adjacent side of your elevation angle, [tex]a[/tex], will be the horizontal distance between you and the birds.
To relate the elevation angle and its opposite and adjacent sides, we must use the trig function tangent:
[tex]tan(32)= \frac{11994}{a} [/tex]
[tex]a= \frac{11994}{tan(32)} [/tex]

We can conclude that your horizontal distance from the birds is 19194.4 feet.