The diagram shows two vertical masts, AB and CD, on horizontal ground. The height of AB is 500m and the height of CD is 350m. The angle of elevation of B from D is 30 degrees. Calculate, to the nearest m, the distance AC.

Given:

The lines AB and CD, on horizontal ground.

The height of AB is 500 m.

The height of CD is 350 m.

The angle of elevation of B from D is 30°

We need to determine the distance AC.

Length of BE:

Let us construct a line that is parallel to AC.

Let the line be ED.

The length of BE is given by

Thus, the length of BE is 150 m

Length of ED:

The length of ED can be determined using the trigonometric ratio.

Thus, we have;

Substituting the values, we get;

Thus, the length of ED is 50√3 m

Length of AC:

From the figure, it is obvious that the sides ED and AC have the equal length.

Thus, we have;

AC = ED = 50√3

Simplifying, we get;

Hence, the length of AC is 86.6 m