Question

A boat leaves the dock and travels 172 meters before dropping the anchor. The angle of depression depends on d, the straight-line distance between the end of the dock and the anchor. Write q as a function of d.

Answer 1

To write q as a function of d, we can use the concept of trigonometry and the angle of depression. The angle of depression is the angle between the line of sight from an observer to an object and the horizontal line. We can use the equation q = arctan(172/d) to represent q as a function of d.

Step-by-step explanation:

To write q as a function of d, we can use the concept of trigonometry and the angle of depression. The angle of depression is the angle between the line of sight from an observer to an object and the horizontal line. In this case, the angle of depression depends on d, the straight-line distance between the end of the dock and the anchor.

Let's assume that the angle of depression is represented by q. From the information given, we know that the boat travels 172 meters before dropping the anchor. This distance is the opposite side of a right triangle, and the horizontal distance between the end of the dock and the anchor is the adjacent side of the triangle.

Using the trigonometric function tangent (tan), we can write the equation:

tan(q) = opposite/adjacent = 172/d

To find q as a function of d, we can solve the above equation for q:

q = arctan(172/d)