Bearings and Right-Triangle Trigonometry

Section 1Bearings

A bearing gives direction from one point to another. It is measured clockwise from north and written with three digits, such as 045 degrees or 270 degrees. Watch out: north is 000 degrees or 360 degrees, east is 090 degrees, south is 180 degrees, and west is 270 degrees.

Section 2Back bearings

A back bearing is the direction for the return journey. If the bearing is less than 180 degrees, add 180 degrees. If it is more than 180 degrees, subtract 180 degrees. Here's the trick: back bearings differ by 180 degrees because they point in opposite directions.

Section 3Elevation and depression

An angle of elevation is measured upwards from a horizontal line, such as looking up at a coconut tree. An angle of depression is measured downwards from a horizontal line, such as looking down from a balcony. The two horizontal lines are parallel, so alternate angle facts often connect them.

Section 4Right-triangle labels

In a right-angled triangle, the hypotenuse is always the side opposite the right angle. The opposite side is across from the angle you are using. The adjacent side touches the angle you are using but is not the hypotenuse.

Section 5SOH-CAH-TOA

SOH-CAH-TOA helps choose the correct trigonometric ratio. Sine = opposite / hypotenuse, cosine = adjacent / hypotenuse, and tangent = opposite / adjacent. Easy to mix up - choose the ratio based on the sides in the question, not the ratio you like best.

Section 6Finding missing sides

To find a missing side, identify the angle, label the sides, choose sine, cosine, or tangent, then solve. If the missing side is on top of the fraction, you usually multiply. If it is on the bottom, you may need to divide carefully.

Section 7Finding missing angles

To find a missing angle, use the inverse trig buttons on a calculator: sin^-1, cos^-1, or tan^-1. First form the correct ratio from the known sides. Then use the inverse function to find the angle, usually rounded to the required accuracy.