Maths: Applications and Interpretation · Geometry and trigonometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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These questions are word problems, so the first step is always a clear labelled diagram. An angle of elevation is measured upwards from the horizontal, and an angle of depression is measured downwards from the horizontal, both at the eye of the observer.
A bearing is a direction given as an angle measured clockwise from north and written with three figures, such as 045°. Draw a north line at every point where a bearing is measured. Then look for right-angled triangles, or use the sine and cosine rules.
An arc is a part of the circumference and a sector is a slice of the circle. Each is the fraction θ/360 of the whole circle.
Students mark the angle of depression between the line of sight and the vertical cliff. It is always measured from the horizontal, so draw the horizontal line at the observer first.
Answer: 20.4 cm (3 significant figures)
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