To calculate the angle of depression, you need to measure the angle between a horizontal line and the line of sight directed downwards.

The angle of depression is an important concept in both trigonometry and geometry. Picture yourself standing on a cliff and looking down at a boat on the water. The horizontal line represents the line that is parallel to the ground at your eye level, while the line of sight is the path from your eyes to the boat. The angle of depression is defined as the angle formed between these two lines.

To determine this angle, you can apply trigonometric ratios if you have certain distance measurements. For instance, if you know the height of the cliff (the opposite side) and the horizontal distance from the base of the cliff to the boat (the adjacent side), you can use the tangent function. The relationship can be expressed as:

In this equation, $\theta$ represents the angle of depression. To solve for $\theta$, you can rearrange the formula:

You can use a scientific calculator to find the inverse tangent (often referred to as arctan) of the ratio. This will yield the angle of depression in degrees.

It’s important to remember that the angle of depression from your perspective is equal to the angle of elevation from the boat’s perspective. This equality arises from the alternate interior angles formed by parallel lines, which can be a useful fact when solving problems involving angles of depression.