Trigonometry in Three DimensionsCalculate sides and angles in three dimensional shapes using trigonometry (including Pythagoras' theorem). 
This is level 1: Three dimensional problems which can be solved using Pythagoras' theorem. You can earn a trophy if you get at least 4 questions correct and you do this activity online. Give answers correct to three significant figures.
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 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy: "I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson." Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." 
Whose Idea Was This?Did you enjoy doing this 'Trigonometry in Three Dimensions' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept. 

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Pythagoras' Theorem  Start by applying Pythagoras' theorem in two dimensions.
2D Trigonometry  Revise using trigonometry in two dimensions.
Level 1  Three dimensional problems which can be solved using Pythagoras' theorem
Level 2  More three dimensional problems requiring the use of trigonometrical ratios
Level 3  Mixed three dimensional problems
Level 4  Worded threedimensional problems without diagrams
Level 5  Problems involving planes (not the flying type!)
ExamStyle 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.
You may also want to use a calculator to check 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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