To answer this question we will use the following diagram as reference:
From the diagram, we get that, to determine h we can use the trigonometric function tangent:
[tex]\tan 68^{\circ}=\frac{80}{h}\text{.}[/tex]
Solving for h, we get:
[tex]h=\frac{80}{\text{tan}68^{\circ}}.[/tex]
Now, to determine h+x we can do an analogous procedure, therefore:
[tex]h+x=\frac{80}{\tan 41^{\circ}}.[/tex]
Finally, we get that:
[tex]x=h+x-h=\frac{80}{\tan41^{\circ}}-\frac{80}{\tan 68^{\circ}}.[/tex]
Simplifying the above result, we get:
[tex]x\approx59.71ft.[/tex]
Answer:
[tex]59.71ft.[/tex]
