Question

Date: The angle of elevation from Nathan to a lighthouse is 74º. If the lighthouse is 112 feet tall, how far is Nathan from the base of the lighthouse?

Answer 1

31.12 feet

Step-by-step 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:

`\begin{gathered} \text{Tan}\theta=\frac{\text{Opposite}}{\text{Adjacent}} \\ \implies\tan 74\degree=(112)/(x) \end{gathered}`

Next, we solve for x:

`\begin{gathered} x\tan 74\degree=112 \\ x=(112)/(\tan 74\degree) \\ x=31.12\text{ feet} \end{gathered}`

The distance between Nathan and the base of the lighthouse is 31.12 feet.