TrigonometrySine, cosine and tangent ratios are used to find sides and angles in rightangled triangles. 
This is level 7: mixed questions (15 questions). You will be awarded a trophy if you get at least 10 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.
InstructionsTry 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. 




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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? Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starteroftheday' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources online we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun." 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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Which Side?  Learn the names of the sides of a rightangled 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/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
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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.
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 doubleclick the 'Check' button to make it float at the bottom of your screen.
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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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.]"