The flag is 31.6 feet from the bottom of the sailboat.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 58°. Assume the opposite side has a length of x feet and the adjacent side has a length of 16 feet.
To determine the length of the opposite side of the triangle, we use the tan of the given angle.
[tex]tan \theta = \frac{oppositeside}{adjacent side} .[/tex]
Step 2:
In the given triangle,
The length of the opposite side = x feet,
The length of the adjacent side = 16 feet,
The angle of the triangle = 58°.
[tex]tan \theta = \frac{oppositeside}{adjacent side} , tan 58 = \frac{x}{16}, tan 58 = 1.6000.[/tex]
[tex]1.6 = \frac{x}{16} , x = (1.6)(16) = 25.6.[/tex]
Since Shianne's eyes are 6 feet from the bottom of the sailboat, the distance between the flag and the bottom of the sailboat [tex]= 25.6 + 6 = 31.6.[/tex]
So the flag is 31.6 feet from the bottom of the sailboat.
