Question

Which is closest to x the distance between the base of the left lighthouse and the boat

Answer 1

From the diagram provided, the angle formed by the onlooker from the top of the lighthouse is 65 degrees (that is 90 degrees minus 25 degrees).

The distance from the base to the top of the lighthouse is 22. That means the reference angle is 65, the adjacent is 22 (the side between the reference angle and the right angle) and the opposite is x (side facing the reference angle).

X can be calculated as follows;

`\begin{gathered} \tan 65=\frac{\text{opp}}{\text{adj}} \\ \tan 65=(x)/(22) \\ \text{Cross multiply and you now have} \\ \tan 65*22=x \\ 2.1445*22=x \\ 47.179=x \\ x\approx47.2 \end{gathered}`

x is approximately 47.2 m

The correct answer is option C