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? 400 feet 200 feet 800 feet 300 feet

We have been given that Max observes the zoo and the library from a helicopter flying at a height of [tex]100\sqrt{3}[/tex] feet above the ground. A zoo and a library are on the ground on the same side of the helicopter.

We can see from our attachment that helicopter, zoo and library forms two right triangles with respect to the ground.

First of all let us find the distance between ground and zoo.

Since we know that tangent relates the adjacent and opposite side of right triangle, so we can set an equation as:

[tex]\text{tan}=\frac{\text{opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(60^o)=\frac{100\sqrt{3}}{y}[/tex]

[tex]y=\frac{100\sqrt{3}}{\text{tan}(60^o)}[/tex]

[tex]y=\frac{100\sqrt{3}}{\sqrt{3}}[/tex]

[tex]y=100[/tex]

Now similarly we will find the distance between ground and library.

[tex]\text{tan}(30^o)=\frac{100\sqrt{3}}{y+x}[/tex]

Upon substituting y=100 we will get,

[tex]\text{tan}(30^o)=\frac{100\sqrt{3}}{100+x}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{100\sqrt{3}}{100+x}[/tex]

[tex]\frac{1}{\sqrt{3}}*\sqrt{3}=\frac{100\sqrt{3}}{100+x}*\sqrt{3}[/tex]

[tex]1=\frac{100*\sqrt{3*3}}{100+x}[/tex]

[tex]1=\frac{100*3}{100+x}[/tex]

[tex]1=\frac{300}{100+x}[/tex]

Upon multiplying both sides of our equation by 100+x we will get,

[tex]1*(100+x)=\frac{300}{100+x}*(100+x)[/tex]

[tex]100+x=300[/tex]

[tex]100-100+x=300-100[/tex]

[tex]x=200[/tex]

Therefore, the distance between library and zoo is 200 feet and option B is the correct choice.

eudora eudora · Answer 2 · 2019-05-05T18:54:30+02:00

Answer:

Option B. 200 feet

Step-by-step explanation:

Max is at point A, flying in a helicopter 100√3 feet above the ground.

Zoo is at point Z and library is at point C on the same side.

Angle formed by the line joining helicopter and zoo with the ground is 60°

Angle formed by the line joining helicopter and library and the ground is 30°.

We have to find the distance between zoo and library.

From ΔABZ

[tex]tan60=\frac{AB}{BZ}=\sqrt{3}[/tex]

Now we know AB = 100√3 feet

We put the value in the formula

[tex]tan60=\frac{100\sqrt{3} }{BZ}=\sqrt{3}[/tex]

BZ = 100 feet

From ΔABC

[tex]tan30=\frac{100\sqrt{3} }{BC}=\frac{1}{\sqrt{3}}[/tex]

BC = 100√3×√3 = 300 feet

Now ZC = BC - BZ = 300 - 100 = 200 feet

Therefore distance between zoo and library is 200 feet.

Option B. is the correct answer.