Question

The height of a flagpole is 22 feet. From a distance of point x on the ground, the angle of elevation is 55°. From a further distance of point y on the ground, the angle of elevation is 20°. What is the distance from point x to point y to the nearest foot?

Answer 1

The distance from x to y is 45ft.

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:

`\tan 55^\circ= (22)/(x)\\\tan 20^\circ = (22)/(y)`

each of which lets us solve for the unknown:

`\tan 55^\circ= (22)/(x) \implies x=(22)/(\tan55^\circ)=15.4ft\\\tan 20^\circ = (22)/(y)\implies y=(22)/(\tan20^\circ)=60.4ft`

The distance from x to y is 60.4-15.4=45ft.