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Trigonometry in Three Dimensions

Calculate sides and angles in three dimensional shapes using trigonometry (including Pythagoras' theorem).

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This is level 4: Worded three-dimensional problems without diagrams. 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.

1. Find the angle that the diagonal from a vertex of a cube makes with an edge of the cube at that vertex.

° Correct Wrong

2. The pyramid ABCDE has a square base ABCD with sides of length 43m and AE = AB = AC = AD = 73m. Find the height of the pyramid.

m Correct Wrong

3. A triangular prism has a cross section in the shape of a right-angled triangle with sides of length 33cm, 44cm and 55cm. The length of the prism is 39cm. PQ is the line from the vertex with the smallest angle of one of the triangular faces to the the vertex with the right angle of the other triangular face. RQ is the edge joining the two vertices at the right angles of the triangular faces. Find the angle between PQ and RQ.

° Correct Wrong

4. A large sports hall is built in the shape of a massive cuboid with a height of 62m, width 47m and length 76m. Find the angle of elevation of one of the top corners of the sports hall as seen from the diagonally opposite corner on the floor of the building.

° Correct Wrong

5. The angle of elevation of the top of a building is 25 degrees from a point X which is due north of the building. The angle of elevation of the top of that same building is 44 degrees from a point Y which is due west of the building. Find the height of the building in metres if the point X is one kilometre further from the building than the point Y.

m Correct Wrong
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This is Trigonometry in Three Dimensions level 4. You can also try:
Level 1 Level 2 Level 3 Level 5

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?

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Answers

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Description of Levels

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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 three-dimensional problems without diagrams

Level 5 - Problems involving planes (not the flying type!)

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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Example

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 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

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