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.
\(Tan\theta = \frac{perpendicular}{Base}\)
\(Tan60^{circ}= \frac{AG}{GB}\)
\(GB = \frac{200\sqrt{3}}{\sqrt{3}}\)
\(GB = 200\)
In ΔAGC
To find GC we will use trigonometric ratio.
\(Tan\theta = \frac{perpendicular}{Base}\)
\(Tan30^{circ}= \frac{AG}{GC}\)
\(GC = \frac{200\sqrt{3}}{\frac{1}{\sqrt{3}}}\)
\(GC =600\)
Now , BC = GC-GB = 600-200=400 feet
Thus the distance between zoo and library is 400 feet
