Question

Max observes the zoo and the library from a helicopter flying at a height of 400 times square root of 3 feet above the ground, as shown below: A helicopter is flying at a height of 400 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?
800 feet 600 feet 200 feet 400 feet

Answer 1

Answer: First option: 800 feet

Solution:

Height: h=400 sqrt(3)

Distance between the zoo and the point in the ground below the helicopter: d1=?

Distance between the library and the point in the ground below the helicopter: d2=?

Distance between the zoo and the library: d=?

d=d2-d1

tan 60°= h/d1

sqrt(3)=400 sqrt(3) / d1

Solving for d1:

sqrt(3) d1 = 400 sqrt(3)

d1= 400 sqrt(3) / sqrt(3)

d1=400

tan 30°= h/d2

sqrt(3) / 3=400 sqrt(3) / d2

Solving for d2: Cross multiplication:

sqrt(3) d2 = 3 [ 400 sqrt(3) ]

sqrt(3) d2 = 1,200 sqrt(3)

d2= 1,200 sqrt(3) / sqrt(3)

d2=1,200

d=d2-d1

d=1,200 feet - 400 feet

d=800 feet

Answer 2

Answer:

800 ft

Step-by-step explanation:

We know that the helicopter is flying $400\sqrt{3}$ feet above the ground.

A zoo and the library are on the same side of the helicopter, each making an angle of 60° and 30° respectively on the line joining the helicopter with the ground.

So we know it makes a right angled triangle with two different angles at the same side and a perpendicular of  $400\sqrt{3}$.

Assuming x to be the distance from helicopter to the library on the ground and y to the distance from helicopter to the zoo on the ground:

$tan 30$° $=\frac{400\sqrt{3} }{x}$

$x = 1200 ft$

$tan 60$° $= \frac{400\sqrt{3} }{y}$

$y= 400 ft$

Distance between the zoo and the library =  x - y = 1200 - 400 = 800 ft