Answer:
400 feet
Step-by-step explanation:
REFER THE ATTACHED FIGURE
Height of the helicopter i.e. AG = 200√3
The angle made by the line joining the helicopter and the zoo with the ground is 60 degrees. i.e.∠ABG = 60°
The angle made by the line joining the helicopter and the library with the ground is 30 degrees i.e.∠ACG = 30°
We are required to calculate the distance between the zoo and the library i.e. BC
In ΔAGB
To find GB we will use trigonometric ratio.
[tex]Tan\theta = \frac{perpendicular}{Base}[/tex]
[tex]Tan60^{circ}= \frac{AG}{GB}[/tex]
[tex]GB = \frac{200\sqrt{3}}{\sqrt{3}}[/tex]
[tex]GB = 200[/tex]
In ΔAGC
To find GC we will use trigonometric ratio.
[tex]Tan\theta = \frac{perpendicular}{Base}[/tex]
[tex]Tan30^{circ}= \frac{AG}{GC}[/tex]
[tex]GC = \frac{200\sqrt{3}}{\frac{1}{\sqrt{3}}}[/tex]
[tex]GC =600[/tex]
Now , BC = GC-GB = 600-200=400 feet
Thus the distance between zoo and library is 400 feet
