Trig Word Problems (Level 1) Score: \( 1 / 8 \) Penalty: none Question A boat is heading towards a lighthouse, whose beacon-light is 145 feet above the water. The boat's crew measures the angle of elevation to the beacon, 11. What is the ship's horizontal distance from the lighth (and the shore)? Round your answer to the nearest tenth of a foot if necessary.

To solve this problem, we can use the tangent function from trigonometry. The angle of elevation corresponds to the triangle formed between the height of the lighthouse, the horizontal distance from the boat to the lighthouse, and the light of the beacon. Specifically, we apply the formula: \[ \tan(\theta) = \frac{\text{opposite (height)}}{\text{adjacent (distance)}} \] Here, \(\theta = 11^\circ\) and the opposite side (height) is 145 feet. Rearranging the formula gives us the distance: \[ \text{distance} = \frac{\text{height}}{\tan(\theta)} = \frac{145}{\tan(11^\circ)} \] Calculating that, we find: \[ \text{distance} \approx \frac{145}{0.1944} \approx 745.2 \text{ feet} \] There you have it! The boat is approximately 745.2 feet away from the lighthouse and shore! Always make sure your calculator is set to degrees when dealing with angles in these problems. A common mistake is using radians by accident which would lead you to an entirely wrong conclusion. So, double-check those settings before diving into your calculations — it saves time and headaches!