Angles of elevation and depression, true bearings, projections and more
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Practice exam-style applied triangle geometry problems
Angles of elevation and depression describe how far upward or downward you look relative to a horizontal line when observing an object.
The angle of elevation is the angle formed by looking upward from the horizontal line to an object above your line of sight.
The angle of depression is the angle formed by looking downward from the horizontal line to an object below your line of sight.
These angles are always measured relative to a horizontal line, never vertical. Because the lines of sight form alternate interior angles with horizontal lines, the angle of elevation from one viewpoint equals the angle of depression from the other viewpoint.
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A true bearing describes a direction measured clockwise from the north direction (0°) around a full circle up to 360°. Bearings are always given using three digits (e.g. 045°,120°,270°) to avoid confusion.
A bearing of 000∘ points directly north.
090∘ points east.
180∘ points south.
270∘ points west.
When working with true bearings, clearly draw a compass rose to visualize directions and measure angles clockwise from the north line.
One very useful fact about bearings is that returning in the direction something came from means adding or subtracting 180° from the original bearing - since it is doing a U-turn.
Whether you add or subtract depends on whether the original bearing is smaller or bigger than 180°, since the resulting bearing must be between 0 and 360°.