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
[tex]BE=AB-AE[/tex]
[tex]BE=500-350[/tex]
[tex]BE=150[/tex]
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;
[tex]tan \ 30^{\circ}=\frac{ED}{BE}[/tex]
Substituting the values, we get;
[tex]\frac{\sqrt{3}}{3}=\frac{ED}{150}[/tex]
[tex]\frac{\sqrt{3}}{3}\times 150=ED[/tex]
[tex]50\sqrt{3}=ED[/tex]
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;
[tex]AC=50 \times 1.732[/tex]
[tex]AC=86.6 \ m[/tex]
Hence, the length of AC is 86.6 m
