To find the angle of elevation from the boat to the top of the lighthouse, we can use the tangent function from trigonometry. The angle of elevation \( \theta \) can be found using the formula:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this scenario, the height of the lighthouse (the opposite side) is 275 feet, and the distance from the boat to the shore (the adjacent side) is 1,324 feet.
Using the formula:
\[ \tan(\theta) = \frac{275}{1324} \]
Calculating the tangent:
\[ \tan(\theta) \approx \frac{275}{1324} \approx 0.207 \]
Next, we find the angle \( \theta \) by taking the arctangent (inverse tangent) of \( 0.207 \):
\[ \theta = \tan^{-1}(0.207) \]
Using a calculator:
\[ \theta \approx 11.7^\circ \]
Rounding to the nearest tenth, the angle of elevation from the boat to the top of the lighthouse is approximately 11.7 degrees.