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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 1: using the sine 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.

1

Correct Wrong

2

Correct Wrong

3

Correct Wrong

4

Correct Wrong

5

Correct Wrong

6

Correct Wrong

7

Diagram
Find the height of a gate if its diagonal forms the hypotenuse of a right-angled triangle and is of length 291cm. The angle marked x is 22°

= cm Correct Wrong

8

In triangle ABC the angle at B is 90°. If AB = 24mm and the angle at C is 32° find the length of the side AC.

AC = mm Correct Wrong

9

In triangle DEF the angle at E is 90°. If DF = 19m and the angle at F is 35° find the length of the side DE.

DE = m Correct Wrong

10

No calculatorThe sine of 30 degrees is one half. Find the length of the hypotenuse of a right-angled triangle if the side opposite the angle of 30° is of length 153cm.

= cm Correct Wrong

Check

This is Trigonometry level 1. You can also try:
Level 2 Level 3 Level 4 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?

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Number Crunch Saga

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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.]"

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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

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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