Answer:
The distance from x to y is 45ft.
Step-by-step explanation:
Use the trigonometric function tangent. In this setting, the tangent of the angle of elevation is the ratio of the flagpole height and the distance of the observer. So we know that for point x and for point y, the following is true:
[tex]\tan 55^\circ= \frac{22}{x}\\\tan 20^\circ = \frac{22}{y}[/tex]
each of which lets us solve for the unknown:
[tex]\tan 55^\circ= \frac{22}{x} \implies x=\frac{22}{\tan55^\circ}=15.4ft\\\tan 20^\circ = \frac{22}{y}\implies y=\frac{22}{\tan20^\circ}=60.4ft[/tex]
The distance from x to y is 60.4-15.4=45ft.
