Trigonometry examples
Use these trigonometry examples to review the method before testing your own triangle question in the app.
What this topic means and what to look for first.
Right-angle trigonometry usually starts by choosing between sine, cosine, and tangent.
The right ratio depends on which sides are known and which side you need.
One reliable route through the topic.
- 1Label the opposite, adjacent, and hypotenuse relative to the chosen angle.
- 2Choose the correct trig ratio.
- 3Substitute the known values carefully.
- 4Rearrange if needed to isolate the unknown side or angle.
- 5Check the answer looks sensible for the triangle.
See the method in action.
Find the opposite side if sin 30 degrees = x / 10
- Use x / 10 = 0.5.
- Multiply both sides by 10.
- So x = 5.
Find the angle if tan theta = 3 / 4
- Use the inverse tangent function.
- theta = tan^-1(3/4).
- So theta is about 36.9 degrees.
Things that commonly send the method off track.
- Choosing the wrong trig ratio because the triangle sides were not labeled first.
- Forgetting to switch to inverse trig when solving for an angle.
Want to test your own problem next?
Use the public page first, then create a free account if you want to try the solver beta on a typed question or photo.
A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Want to try a similar problem yourself?
Create a free account if you want to use the solver beta after reading the guide.
A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Extra geometry revision resources
These printed-resource searches are useful if you want more diagrams and geometry practice than one page can provide.
Amazon
Geometry workbook search
Useful for shape, angle, and diagram-heavy practice when you want more than a single online example set.
View Geometry workbook searchAmazon
Trigonometry revision book search
A practical follow-up if you want more triangle, sine, cosine, and tangent examples in print.
View Trigonometry revision book searchFound this useful?
Share the page with someone who is searching for the same maths topic before they go straight to a solver.
Short answers worth checking.
Many people use SOHCAHTOA as a quick memory aid for sine, cosine, and tangent.
Yes, for most GCSE-style triangle questions the calculator should be in degrees mode.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.