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Basile [38]
4 years ago
8

Max observes the zoo and the library from a helicopter flying at a height of 200 times square root of 3 feet above the ground, a

s shown below: A helicopter is flying at a height of 200 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? (1 point) HELPPPP!!!
400 feet

200 feet

600 feet

800 feet

Mathematics
2 answers:
juin [17]4 years ago
7 0

Answer:

The distance between the zoo and the library is 400ft

Step-by-step explanation:

Let x be the distance between point G and the zoo

Let y be the distance between the zoo and the library

To solve this problem quickly, we use trigonometric relations

tan(angle) = opposite cathetus / adjacent cathetus

In this case

tan(30) = (200√3) / (x+y)

(x+y) =  (200√3)/ tan(30)

(x+y) = 600 ft

For the other angle

tan(60) = (200√3) / (x)

(x) =  (200√3)/ tan(60)

x = 200 ft

y = 600 ft - 200 ft = 400 ft

The distance between the zoo and the library is 400ft

ELEN [110]4 years ago
6 0

Answer:

The correct option is A.

Step-by-step explanation:

Let the distance between the zoo and the library is x.

In a right angled triangle,

\tan \theta = \frac{opposite}{adjacent}

In triangle ABG,

\tan (30^{\circ}) = \frac{AG}{GB}

\frac{1}{\sqrt{3}} = \frac{200\sqrt{3}}{GB}

On cross multiplication, we get

GB\times 1=\sqrt{3}\times 200\sqrt{3}

GB=600

In triangle AGC,

\tan (60^{\circ}) = \frac{AG}{GC}

\sqrt{3} = \frac{200\sqrt{3}}{GC}

On cross multiplication, we get

GC\times \sqrt{3}=200\sqrt{3}

Divide both sides by √3.

GC=200

The distance between the zoo and the library is

CB=GB-GC

x=600-200

x=400

The distance between the zoo and the library is 400 feet. Therefore the correct option is A.

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