Background: Trigonometry

The lengths of the sides and the sizes of the angles of a right-angled triangle are connected mathematically by what we call trigonometrical relationships. There are three main relationships. The sine function The cosine function The tangent function

Find an angle

If two sides of a right-angled triangle are known then you can find the size of any of the angles. Follow these steps. 1. Two sides of a triangle are known. 2. Decide which angle to find and label it q 3. Label the two known sides appropriately as either opposite (o), adjacent (a) or hypotenuse (h). 4. Quote the correct trigonometry formula that uses these two sides. cos q=a/h 5. Substitute in the known values. cos q=7/12 6. Use a calculator to find the value of q. Press INV COS (7÷12) or the equivalent on your calculator. 7. Round off your answer to a suitable accuracy. q=54.3 degrees.

Find a side

If the angles in a right-angled triangle and one of the sides are known, then you can find the length of either of the other sides. Follow these steps. 1. A side and an angle of a triangle are known. 2. Decide which other side to find and label it x 3. Label the two sides appropriately as either opposite (o), adjacent (a) or hypotenuse (h). 4. Quote the correct trigonometry formula that uses these two sides. sin q=o/h 5. Substitute in the known values. sin 60=x/12 6. Use a calculator to find the value of x. Press 12 × SIN 60 or the equivalent on your calculator. 7. Round off your answer to a suitable accuracy. x=10.4 cm.

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