Question

a ship is sailing along the east coast of new york. the ships navigator sights a lighthouse on land. the line of sight forms a right angle with the ships line of travel. find the bearing of the lighthouse for the course given. 1. 26° 2. 196° 3. 307°

Explanation:

Step1: Recall bearing rules

Bearings are measured clock - wise from the north.

Step2: Analyze case 1

If the ship's course is $26^{\circ}$, and the line of sight to the lighthouse is at a right - angle to the line of travel. If the ship is moving at $26^{\circ}$, the bearing of the lighthouse (since it's at a right - angle) is $26^{\circ}+90^{\circ}=116^{\circ}$ (if the lighthouse is to the right of the ship's path). But if we consider the standard bearing convention, we might also have $26^{\circ} + 270^{\circ}=296^{\circ}$ depending on the side of the path the lighthouse is on. However, assuming the most common situation where the lighthouse is in the direction of the right - hand side of the ship's path relative to the forward motion, we consider the addition of $90^{\circ}$.

Step3: Analyze case 2

If the ship's course is $196^{\circ}$, and the line of sight to the lighthouse is at a right - angle. If we add $90^{\circ}$ to $196^{\circ}$, $196^{\circ}+90^{\circ}=286^{\circ}$.

Step4: Analyze case 3

If the ship's course is $307^{\circ}$, and the line of sight to the lighthouse is at a right - angle. Adding $90^{\circ}$ to $307^{\circ}$, we get $307^{\circ}+90^{\circ}=397^{\circ}$. Since bearings are usually in the range of $0^{\circ}$ to $360^{\circ}$, $397^{\circ}-360^{\circ} = 37^{\circ}$.

Answer:

1. $116^{\circ}$
2. $286^{\circ}$
3. $37^{\circ}$