Question Video: Identifying the Angle of Elevation in a Diagram Mathematics

In the given diagram of a ladder leaning against a wall, which of the following angles represents the ladder’s angle of elevation? [A] ∠𝐴𝐵𝐶 [B] ∠𝐴𝐶𝐵 [C] ∠𝐵𝐴𝐶

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Video Transcript

In the given diagram of a ladder leaning against a wall, which of the following angles represents the ladder’s angle of elevation? Angle 𝐴𝐵𝐶, angle 𝐴𝐶𝐵, or angle 𝐵𝐴𝐶.

Let’s begin by discussing what we mean by an angle of elevation. This is defined to be an angle measured from the horizontal up towards an object. We may say it’s the angle between the horizontal and the line of sight as we look up towards something. This is in contrast to an angle of depression, which is the angle between the horizontal and the line of sight when we look down towards something.

Let’s consider then this diagram of a ladder. The horizontal is this line here. Standing at point 𝐴, the angle of elevation is formed when we look up from the horizontal towards the top of the ladder, which is point 𝐵. The angle of elevation then is this angle here. We can describe this angle using three letters, either as angle 𝐶𝐴𝐵 or as angle 𝐵𝐴𝐶. This is option (c) of the three options we were given.

At this point, we’ll also just point out that angle 𝐴𝐵𝐶 on the diagram, that’s this angle here, is not an angle of depression. It’s a common mistake to assume that it is. But remember, angles of elevation and depression must both be measured from the horizontal. If we stood at the top of the ladder and looked down towards the bottom of the ladder, the angle of depression would in fact be this angle here, measured from the horizontal down towards point 𝐴. In fact, the measure of this angle of depression would be the same as the measure of the angle of elevation because they are alternate angles in parallel lines.

Our answer to the question, which of the following angles represents the ladder’s angle of elevation, is angle 𝐵𝐴𝐶.

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