Watch out
Using the side labels relative to the wrong angle.
Scottish National 5 Mathematics
National 5 Maths Right-angled trigonometry
Use sine, cosine and tangent to find sides and angles in right-angled triangles.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Label opposite, adjacent and hypotenuse relative to the given angle.
- Use degree mode and keep full calculator values until the final requested rounding.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Right-angled trigonometry is an assessed part of Scottish National 5 Mathematics in the trigonometry area. Use sine, cosine and tangent to find sides and angles in right-angled triangles.
Label opposite, adjacent and hypotenuse relative to the given angle.
Choose the ratio containing the known and unknown sides.
Use inverse trig when the unknown is an angle.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Visual support
SOH CAH TOA
Key formulae and rules
- sin x = opposite ÷ hypotenuse
- cos x = adjacent ÷ hypotenuse
- tan x = opposite ÷ adjacent
Check
Check that the labelled opposite, adjacent and hypotenuse sides are relative to the stated angle, and that the answer is sensible for the diagram.
Exam tip
Show the selected relationship and substitution before calculating, then give every required angle or unit.
Calculator tip
Use degree mode and keep full calculator values until the final requested rounding.
Worked examples
Worked example 1
Right-angled trigonometry worked example
A right triangle has opposite 8 cm and adjacent 15 cm. Find the angle.
- tan x =
- x = tan−1
Answer: 28.1°
Watch out
- Using the side labels relative to the wrong angle.
- Leaving the calculator in radian mode.