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Trigonometry

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

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This is level 4: using the sine ratio to find an angle (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.

1

Correct Wrong

2

Correct Wrong

3

Correct Wrong

4

Correct Wrong

5

Correct Wrong

6

Correct Wrong

7

Diagram
Find x.

x = ° Correct Wrong

8

In triangle ABC the angle at B is 90°. If AB = 22mm and AC = 36mm find the size of the angle at C in degrees.

angle C = ° Correct Wrong

9

In triangle DEF the angle at E is a right angle. If DE = 23mm and DF = 36mm find the size of the angle at F in degrees.

angle F = ° Correct Wrong

10

A kite flying at a height of 25m above the ground is attached to a string of length 45m which is attached to a peg in the ground. What angle does the string make with the horizontal?

angle = ° Correct Wrong

Check

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

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

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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Practice Papers

Practice Papers

Mathematics GCSE(9-1) Higher style questions and worked solutions presented as twenty short, free, practice papers to print out.

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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

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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.

Example

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