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Sine, cosine and tangent ratios are used to find sides and angles in right-angled triangles.

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This is level 3: using the tangent ratio to find a side (10 questions). You will be awarded a trophy if you get at least 7 correct and you do this activity online.  Give your answers correct to three significant figures. For the first six questions find the value of \(x\). Diagrams are not to scale.


Correct Wrong


Correct Wrong


Correct Wrong


Correct Wrong


Correct Wrong


Correct Wrong


Find distance, d, if the height of the tree is 5.1m and the angle marked A is 28°.

d = m Correct Wrong


In triangle ABC the angle at B is 90°. If BC = 18mm and the angle at C is 40° find the length of the side AB.

AB = mm Correct Wrong


In triangle DEF the angle at E is 90°. If DE = 39m and the angle at F is 57° find the length of the side FE.

FE = m Correct Wrong


No calculatorThe tangent ratio of 45 degrees is one. Find the length of the opposite side of a right-angled triangle if the side adjacent the angle of 45° is of length 176cm.

= cm Correct Wrong


This is Trigonometry level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7 Level 8


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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if should go offline for whatever reason, there is a mirror site at that contains most of the resources that are available here on

When planning to use technology in your lesson always have a plan B!

Joseph, Pleasanton

Tuesday, February 28, 2023

"It asked for the acute angle of diagonals in a rectangle with side lengths 3 and 9, so I typed in the answer to arctan(3/9) which is 18.4, but it kept saying I was wrong. Please help!

[Transum: Hi Joseph, I think you have found the angle between a diagonal and one of the sides of the rectangle. Read the question again carefully as that is not what is required.]"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


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Description of Levels



Which Side? - Learn the names of the sides of a right-angled triangle before beginning trigonometry.

Level 1 - Using the sine ratio to find a side (10 questions)

Level 2 - Using the cosine ratio to find a side (10 questions)

Level 3 - Using the tangent ratio to find a side (10 questions)

Level 4 - Using the sine ratio to find an angle (10 questions)

Level 5 - Using the cosine ratio to find an angle (10 questions)

Level 6 - Using the tangent ratio to find an angle (10 questions)

Level 7 - Mixed questions (15 questions)

Level 8 - Review exercise (20 questions)

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


You will want to use a calculator for your working. See Calculator Workout skill 11.

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