In this diagram, one person is standing at point A, one person is at point B, and both are looking at a helicopter at point C. The helicopter is 1000 feet above the ground on which the two people are standing.

A. If the angle of elevation at point A is 60 degrees and the angle of elevation at point B is 20 degrees, approximately how many feet apart are A& B?

x=x₁+x₂= 1000sin60 =100sin20=

=1000(sin60+sin20)=
=1000(0.866+0.342)=1208 feet

To find the approximate distance between points A and B, we need to use trigonometry and the angles of elevation provided.

First, let's label the height of the helicopter as "h" and the distance between points A and B as "x."

We can create a right-angled triangle with point C being the top vertex, point A being the bottom left vertex, and point B being the bottom right vertex.

Now, we can use the tangent function to find the relationship between the angle of elevation and the sides of the triangle.

In triangle ABC, the tangent of the angle of elevation at point A is given by:

tan(60°) = h / x

Similarly, the tangent of the angle of elevation at point B is given by:

tan(20°) = h / (x + d)

where "d" is the distance between A and B. Notice that we added "d" to the x because it represents the additional distance from x to reach point B.

Now, we can solve these equations to find the value of "x."

First, we rearrange the equation for tan(60°):

x = h / tan(60°)

Next, we rearrange the equation for tan(20°):

(x + d) = h / tan(20°)

From these two equations, we can substitute the value of "h" as 1000 feet, and then calculate the value of "x" and "d."

Finally, we can find the approximate distance between A and B by adding "x" and "d."

Please note that these calculations assume a level ground surface and neglect any height differences between points A and B.