Final answer:
The bearing of the lighthouse L from the ship at A is calculated using trigonometry and is found to be approximately 213 degrees.
Step-by-step explanation:
To calculate the bearing of the lighthouse L from the ship at A, we need to use trigonometry.
Since the ship is 10.6 km west of L, this distance represents the horizontal side of a right-angled triangle, where A is the right angle, and the hypotenuse is the distance from the ship to the lighthouse, which is 12.5 km.
Using trigonometry, specifically the cosine of the angle we're looking for (let's call it θ), we can set up the equation:
cos(θ) = adjacent/hypotenuse
= 10.6/12.5
To find θ, we take the inverse cosine (arcos) of (10.6/12.5):
θ = cos⁻¹(10.6/12.5)
We then use a calculator to find that θ is approximately 57 degrees.
However, bearings are measured from the north, going clockwise.
The line from L to A is west of L, so we need to subtract our angle from 270 degrees (the bearing just west of north).
Bearing of L from A = 270° - θ
Bearing of L from A = 270° - 57°
Bearing of L from A = 213°