Question

Max observes the zoo and the library from a helicopter flying at a height of 300 times square root of 3 feet above the ground, as shown below:
What is the distance between the zoo and the library?

300 feet
600 feet
900 feet
100 feet

Answer 1

600 feet is your answer

Answer 2

For this case, the first thing to do is find the horizontal distance from the plane to the zoo and the library respectively.
 We then have the following trigonometric relationships:
 For the zoo:
 $tan (60) = (300 * root (3)) / d1$ 
 Clearing d1 we have:
 $d1 = (300 * root (3)) / tan (60) d1 = 300$
 For the library:
 $tan (30) = (300 * root (3)) / d2$ 
 Clearing d1 we have:
 $d2 = (300 * root (3)) / tan (30) d2 = 900$
 Then, the distance between zoo and library is:
 $d2 - d1 = 900 - 300 d2 - d1 = 600 feet$
 Answer:
 The distance between the zoo and the library is:
 600 feet