Answer:
31.12 feet
Explanation:
The diagram illustrating this problem is attached below:
The distance between Nathan and the base of the lighthouse is labeled x above.
From trigonometric ratios:
[tex]\begin{gathered} \text{Tan}\theta=\frac{\text{Opposite}}{\text{Adjacent}} \\ \implies\tan 74\degree=\frac{112}{x} \end{gathered}[/tex]
Next, we solve for x:
[tex]\begin{gathered} x\tan 74\degree=112 \\ x=\frac{112}{\tan 74\degree} \\ x=31.12\text{ feet} \end{gathered}[/tex]
The distance between Nathan and the base of the lighthouse is 31.12 feet.
