Transum Software

Trigonometry

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

  Menu   Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Exam-Style Help More

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.

1

Correct Wrong

2

Correct Wrong

3

Correct Wrong

4

Correct Wrong

5

Correct Wrong

6

Correct Wrong

7

Diagram
Calculate the size in degrees of angle QRP if:

    PQ = 120 metres;
    QR = 200 metres;
    RP = 160 metres.

angle QPR = ° Correct Wrong

8

In triangle ABC the angle at B is 90°. If BC = 38mm and AB = 24mm find the size of the angle at C in degrees.

angle C = ° Correct Wrong

9

In triangle DEF the angle at E is 90°. If DF = 21m and the angle at F is 68° find the length of the side DE.

DE = m Correct Wrong

10

Diagram
Calculate the length of the hypotenuse of this right-angled triangle if the length of the base (shown as d in the diagram) is 37 metres.

= m Correct Wrong

11

Miriam is lying on a flat, horizontal beach looking up at the top of a 34m high cliff which is 42m away. Find the angle of elevation of the top of the cliff from Miriam's position on the beach.

angle = ° Correct Wrong

12

Diagram
The diagram shows an isosceles triangle. The equal angles, x, are each 84 degrees and the equal sides, f, are each 16 metres.
Find the length of the shorter side of the triangle marked as d.

[Hint: Sketch a horizontal line on the diagram to split the isosceles triangle into two right-angled triangles.]

d = m Correct Wrong

13

Find the smallest angle of an isosceles triangle that has one side of length 2.8cm and two sides of length 6.5cm.

[Hint: Draw a sketch of the isosceles triangle then sketch its line of symmetry to split the isosceles triangle into two right-angled triangles.]

angle = ° Correct Wrong

14

DiagramFind m if n = 72cm, p = 40° and s = 23°.

m = cm Correct Wrong

15

In triangle PQR there is a right-angle at Q. The side PQ is twice as long as side QR. Calculate the size of angle RPQ.

angle RPQ = ° Correct Wrong

Check

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

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

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 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Connect 4 Factors

Connect 4 Factors

A mathematical version of the popular Connect 4 game based on getting four numbers with a common factor in a line. Fun for one, two or a whole class of pupils.

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

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:

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 Transum.org should go offline for whatever reason, there are mirror sites at Transum.com and Transum.info that contain most of the resources that are available here on Transum.org.

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

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.

Apple

©1997-2021 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2021
Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://Transum.org/go/?Num=71

Description of Levels

Close

Close

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.

Log in Sign up

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.

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.

Log in Sign up

Close

Close