Final answer:
The recommended bow angle for measuring the perpendicular distance to a landmark is 90 degrees; this right angle with a baseline is essential in trigonometric calculations for surveying and navigation.
Step-by-step explanation:
The recommended measurement of your bow angle when recording the perpendicular distance from a landmark to the path of your boat is 90 degrees. This is because a perpendicular line forms a right angle with a baseline, which is exactly 90 degrees. In surveying, establishing such a baseline and then measuring angles from this line is a common practice to determine distances to objects. For instance, a surveyor measuring the width of a river would start by establishing a baseline along the bank of the river. If they then measure an angle less than 90 degrees from this baseline to a tree across the river, they can calculate the river's width using trigonometric relationships in a right-angled triangle.
Similarly, using two observation points to form a baseline and then applying the concept of parallax, the change in direction of a landmark from different vantage points can be observed. This allows for calculating the distance to the landmark accurately. Navigational practices, such as using tools like a sextant for determining the angle between the sun and the horizon, rely on these same principles of angle measurement for positioning.