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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 = 17mm and AC = 33mm 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 = 37mm and DF = 53mm find the size of the angle at F in degrees.

angle F = ° Correct Wrong

10

A kite flying at a height of 20m above the ground is attached to a string of length 35m 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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Featured Activity

Remainder Race

Remainder Race

A brilliant game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number. There are one and two player versions and the rules are inspired by the Royal Game of Ur.

Answers

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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

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.

Teachers

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:

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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.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

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

Example

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

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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