Answer:
Approximately [tex]171\; {\rm ft}[/tex]
Step-by-step explanation:
Refer to the diagram attached. The [tex]55^{\circ}[/tex] degree can be considered as an angle in a right triangle consisting of:
- Hypotenuse: the line segment joining the top of the two buildings.
- Leg adjacent to the [tex]55^{\circ}[/tex] angle: height difference between the two buildings.
- Leg opposite to the [tex]55^{\circ}[/tex] angle: horizontal distance between the two buildings.
Given the height of the two buildings, the difference between their heights would be [tex](320\; {\rm ft} - 200\; {\rm ft})[/tex]. The goal is to find the length of horizontal distance between the two buildings. To do so, make use of the fact that in this right triangle, the tangent of [tex]55^{\circ}[/tex] angle is equal to the ratio between the length of the leg opposite to this angle, and the length of the leg adjacent to this angle:
[tex]\begin{aligned}\tan(55^{\circ}) &= \frac{(\text{opposite leg})}{(\text{adjacent leg})} \\ &= \frac{(320\; {\rm ft} - 200\; {\rm ft})}{(\text{horizontal distance})}\end{aligned}[/tex].
Rearrange this equation to find the horizontal distance between the two buildings:
[tex]\begin{aligned} & (\text{horizontal distance}) \\ =\; & (320\; {\rm ft} - 200\; {\rm ft})\, \tan(55^{\circ}) \\ \approx\; & 171\; {\rm ft}\end{aligned}[/tex].
In other words, the horizontal distance between the two buildings would be approximately [tex]171\; {\rm ft}[/tex].
