the distance the ship travelled from point A to D is 582 ft
Explanation:To dtermine the distance from point A to D, we need to find the distance from point A to C and distance from point C to D
To get the distance from point C to D, we will consider triangle BCD:
opposite = 125 ft
DC = ?
angle = 16°
To get DC (adjacent), we will use tan ratio:
[tex]\begin{gathered} \tan \text{ 16}\degree\text{ = }\frac{opposite}{adjacent} \\ \tan \text{ 16}\degree\text{= }\frac{125}{DC} \\ DC(\tan \text{ 16}\degree)\text{ = 125} \\ DC\text{ = }\frac{125}{\tan\text{ 16}\degree} \\ DC\text{ = }435.93\text{ ft} \end{gathered}[/tex]To get the distance from point A to C, we will consider triangle ABC:
opposite = 125 ft
AC = ?
angle = 7°
To get AC (adjacent), we will use tan ratio:
[tex]\begin{gathered} \tan \text{ 7}\degree\text{ = }\frac{opposite}{adjacent} \\ \tan \text{ 7}\degree\text{= }\frac{125}{AC} \\ AC(\tan \text{ 7}\degree)\text{ = 125} \\ AC\text{ = }\frac{125}{\tan\text{ 7}\degree} \\ AC\text{ = }1018.04\text{ ft} \end{gathered}[/tex]Distance AC = Distance DC + Distance AD
[tex]\begin{gathered} 1018.04\text{ = 435.93 + Distance AD} \\ \text{Distance AD = 1018.04 - 435.93} \\ \text{Distance AD = 582.11 ft} \end{gathered}[/tex]The distance the ship travelled from point A to D = Distance AD
To the nearest foot, the distance the ship travelled from point A to D is 582 ft