Trigonometry and Bearings
Trigonometry and bearings
Right-angled trigonometry uses sine, cosine and tangent: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. You must choose the correct ratio, find missing sides and angles, and solve problems involving angles of elevation and depression. For non-right triangles, know the sine rule, cosine rule and area formula. Bearings are measured clockwise from north and written with three figures, so north is 000 degrees and east is 090 degrees. Back-bearings differ by 180 degrees.
Traps include using the wrong side as opposite, having the calculator in the wrong angle mode, and misreading a bearing from a diagram. The angle of depression is measured downwards from the horizontal, not from the vertical. When using the sine rule, pair a side with its opposite angle. Bearings must be given as three digits, for example 045 not 45. In a triangle, check whether the question requires the obtuse possibility.
Worked example: a ladder 5 m long makes an angle of 60 degrees with the ground. The height reached is the side opposite the angle, so height = 5 sin 60 = 4.33 m to 3 significant figures. If point B is on a bearing of 050 degrees from A, then the bearing of A from B is 050 + 180 = 230 degrees.
Rule of thumb: label the sides relative to the angle before choosing sine, cosine or tangent, and sketch the north line at every bearing point.