Disclaimer: This app is for personal, casual, and hobby use. It is provided 'as-is' without warranties of accuracy; use for educational purposes is not intended.
geometry

Trigonometry examples

Use these trigonometry examples to review the method before testing your own triangle question in the app.

Quick explanation

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.

Step-by-step method

One reliable route through the topic.

  1. 1Label the opposite, adjacent, and hypotenuse relative to the chosen angle.
  2. 2Choose the correct trig ratio.
  3. 3Substitute the known values carefully.
  4. 4Rearrange if needed to isolate the unknown side or angle.
  5. 5Check the answer looks sensible for the triangle.
Worked examples

See the method in action.

Example 1

Find the opposite side if sin 30 degrees = x / 10

  1. Use x / 10 = 0.5.
  2. Multiply both sides by 10.
  3. So x = 5.
Example 2

Find the angle if tan theta = 3 / 4

  1. Use the inverse tangent function.
  2. theta = tan^-1(3/4).
  3. So theta is about 36.9 degrees.
Common potential mistakes

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.
Follow-up access

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.

Follow-up access

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.

External revision resources

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 search

Amazon

Trigonometry revision book search

A practical follow-up if you want more triangle, sine, cosine, and tangent examples in print.

View Trigonometry revision book search
Share this page

Found this useful?

Share the page with someone who is searching for the same maths topic before they go straight to a solver.

FAQ

Short answers worth checking.

How do I remember which ratio to use?

Many people use SOHCAHTOA as a quick memory aid for sine, cosine, and tangent.

Do I need my calculator in degrees mode?

Yes, for most GCSE-style triangle questions the calculator should be in degrees mode.

Related guides

Continue with the next closely related topic.

Next places to browse

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.