Max observes the zoo and the library from a helicopter flying at a height of 100 times square root of 3 feet above the ground, as shown below.

A helicopter is flying at a height of 100 multiplied by square root of 3 feet above the ground. A zoo and a library are on the ground on the same side of the helicopter. The angle made by the line joining the helicopter and the zoo with the ground is 60 degrees. The angle made by the line joining the helicopter and the library with the ground is 30 degrees.

What is the distance between the zoo and the library?

Question

Max observes the zoo and the library from a helicopter flying at a height of 100 times square root of 3 feet above the ground, as shown below.
 
A helicopter is flying at a height of 100 multiplied by square root of 3 feet above the ground. A zoo and a library are on the ground on the same side of the helicopter. The angle made by the line joining the helicopter and the zoo with the ground is 60 degrees. The angle made by the line joining the helicopter and the library with the ground is 30 degrees.
 
What is the distance between the zoo and the library?

anonymous · Answer

I have found that the adjacent to 60 degrees is 100, then the hypotenuse would be 200. So on the other triangle, you could use that length to find the adjacent of the 30 degree triangle using the tangent; however, I solved it and it wasn't one of the answer choices. Could someone please steer me in the correct direction?

ganpat · Answer

use trigonometric formulas..

|dw:1343067255962:dw|
from the figure, 

tan 30 = 100 (sq rt 3)/ GL
GL =   100 (sq rt 3)/ tan 30

similarly, 

tan 60 =  100 (sq rt 3)/ GZ
GZ =  100 (sq rt 3)/ tan 60

Find the values , and distance between Zoo and library =  ZL = GL - GZ...