Question

A boat sails directly away from a skyscraper located on the edge of a large lake. The skyscraper is 120 meters tall. A photographer on the boat is taking pictures of the skyscraper with a camera that has a 28° viewing lens.

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} Height(h)=120m \\ \theta=28^(\circ) \\ d=\text{?} \end{gathered}`

We will use the Trigonometric ratio (SOHCAHTOA) to solve for d. In this case, we will use ''TOA''

`\begin{gathered} TOA\Rightarrow tan\theta=(opposite)/(adjacent) \\ tan\theta=(opposite)/(adjacent) \\ opposite\Rightarrow height=120m \\ adjacent\Rightarrow d \\ \theta=28^(\circ) \\ tan28^(\circ)=(120)/(d) \\ d\cdot tan28^(\circ)=120 \\ d=(120)/(tan28^(\circ))=225.687\approx226 \\ d=226m \end{gathered}`