Question

max observes the zoo and the library from a helicopter flying at a height of $200sqrt{3}$ feet above the ground, as shown: what is the distance between the zoo and the library? (1 point) 400 feet 200 feet 600 feet 800 feet

Explanation:

Step1: Find distance G to Library

Use tan(30°) = opposite/adjacent
$\tan(30^\circ) = \frac{200\sqrt{3}}{GL}$
$\frac{1}{\sqrt{3}} = \frac{200\sqrt{3}}{GL}$
$GL = 200\sqrt{3} \times \sqrt{3} = 200 \times 3 = 600$ feet

Step2: Find distance G to Zoo

Use tan(60°) = opposite/adjacent
$\tan(60^\circ) = \frac{200\sqrt{3}}{GZ}$
$\sqrt{3} = \frac{200\sqrt{3}}{GZ}$
$GZ = \frac{200\sqrt{3}}{\sqrt{3}} = 200$ feet

Step3: Calculate Zoo to Library distance

Subtract GZ from GL
$GL - GZ = 600 - 200$

Answer:

400 feet