Application of trigonometry
Once you are comfortable using the trigonometric relationships from the earlier pages of this guide it is important that you practise their application. In your exam you will be expected to apply your knowledge to a range of contexts including 3D shapes and bearings.
Question
Find the size of the angle at B.
Since we know the length of the adjacent and opposite sides we need to use tan to calculate the missing angle.
\({tan~θ} = \frac {opposite} {adjacent}\)
So \({tan~θ} = \frac {4} {3}\)
Using inverse tan (tan-1 on a calculator) we find θ = 53.13° (to two decimal places).
Question
Tim walks 5 m north then 3 m east. What is the bearing of where he ends up from where he started?
If we take Tim’s path it traces out two sides of a triangle with the missing side being the hypotenuse:
Since we know the length of the adjacent and opposite sides we need to use tan to calculate the missing angle.
\({tan~θ} = \frac {opposite} {adjacent}\)
So \({tan~θ} = \frac {3} {5}\)
Using inverse tan (tan-1 on a calculator) we find θ = 31° (to the nearest degree).
So the bearing is 031° (remembering that bearings are always 3 figures).
More guides on this topic
- Loci and constructions - WJEC
- Pythagoras' theorem - Intermediate & Higher tier - WJEC
- Enlargements/Similar shapes - Intermediate & Higher tier - WJEC
- Maps - WJEC
- Conversion between metric and imperial units - WJEC
- Dimensional analysis - Intermediate & Higher tier - WJEC
- Compound measures - WJEC
- Perimeter and area - WJEC
- Surface area and volume - WJEC
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