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href="../2398/31-volume-and-surface-area.html">3.1 Volume and surface area</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2260/32-right-angled-trigonometry.html">3.2 Right angled Trigonometry</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2261/32-non-right-angled-trigonometry.html">3.2 Non-right angled trigonometry</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2196/33-applications-of-trigonometry.html">3.3 Applications of trigonometry</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1862/34-circles.html">3.4 Circles</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2120/35-36-perpendicular-bisectors-voronoi-diagrams-.html"> 3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams </a></label></li></ul></li><li class=""><label 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14px"><i class="fa fa-fw"></i><a href="../2258/45-46-probability.html">4.5 & 4.6 Probability</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2190/47-discrete-random-variables.html">4.7 Discrete random variables</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2403/48-binomial-distribution.html">4.8 Binomial Distribution</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2191/49-normal-distribution.html">4.9 Normal Distribution</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2407/410-spearmans-rank-correlation-coefficient.html">4.10 Spearman's Rank Correlation Coefficient</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2259/411-chi-squared-independence-tests.html">4.11 Chi Squared Independence tests</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2413/411-chi-squared-goodness-of-fit-and-the-t-test.html">4.11 Chi Squared Goodness of Fit and the T-Test</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../1078/calculus.html">Calculus</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2400/51-53-introduction-to-calculus.html">5.1 & 5.3 Introduction to Calculus</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2401/52-54-tangents-normals-and-the-second-derivative.html">5.2 & 5.4 Tangents, normals and the second derivative</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2402/56-57-stationary-points-and-optimisation.html">5.6 & 5.7 Stationary Points and Optimisation</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2197/55-58-integration-and-trapezoidal-rule.html">5.5 & 5.8 Integration and Trapezoidal rule</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../2800/pre-ib-preparation-.html">Pre-IB Preparation </a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2812/pre-ib-weekly-quiz-1.html">Pre-IB Weekly Quiz 1</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2814/pre-ib-weekly-quiz-2.html">Pre IB Weekly Quiz 2</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2815/pre-ib-weekly-quiz-3.html">Pre-IB Weekly Quiz 3</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../2819/pre-ib-weekly-quiz-4.html">Pre-IB Weekly Quiz 4</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../1082/exams-assessment.html">Exams & Assessment</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1083/ia-technology.html">IA & technology</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1085/exam-advice.html">Exam Advice</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1084/sixes-sevens.html">Sixes & sevens</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../2928/for-teachers.html">For Teachers</a></label></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Geometry and Trigonometry <a href="#" class="mark-page-favorite pull-right" data-pid="1070" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i> Home</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Geometry and Trigonometry</span></li> </ol> <article id="main-article"> <div class="greyBg"> <h2><img alt="" src="../../images/dans-images/trig.png" style="width: 160px; height: 140px; float: left;">The physical world in shape and space</h2> <p>So many applications of mathematics depend on understanding shape and space. This geometry and trigonometry module gets to the heart of that. For many, much of this will be a review of work you have done before with trigonometry, missing sides and missing angles, cirles and volume and surface area of 3d shapes. Where it might be new is with specific applications in and out of 3 dimensions. Also, dividing up space with Voronoi diagrams will be new to most!</p> </div> <h2>What is in this section?</h2> <div class="index-list"> <div class="item"> <div class="bg-cover cover-96" onclick="window.location='/mathsapplications/page/2398/31-volume-and-surface-area'" style="background-image: url('../../files/GT/vsa/vsa.jpg')" title="3.1 Volume and surface area"> </div> <div class="content"> <h4 class="head"><a href="../2398/31-volume-and-surface-area.html">3.1 Volume and surface area</a></h4> <p class="body">This section is all about the volume and surface area of prisms, cylinders, pyramids, cones and spheres! All of these shapes has their own unique properties and this section is about understanding and calculating the volumes and surface areas.</p> </div> </div> <div class="item"> <div class="bg-cover cover-96" onclick="window.location='/mathsapplications/page/2260/32-right-angled-trigonometry'" style="background-image: url('../../files/GT/RAT/Rat2-small.jpg')" title="3.2 Right angled Trigonometry"> </div> <div class="content"> <h4 class="head"><a href="../2260/32-right-angled-trigonometry.html">3.2 Right angled Trigonometry</a></h4> <p class="body">This part of trigonometry can be seen in the recurring relationships between the sides of right angles triangles. The relationship means that we can use two bits of information about a triangle to work out a third and so on until we know everything...</p> </div> </div> <div class="item"> <div class="bg-cover cover-96" onclick="window.location='/mathsapplications/page/2261/32-non-right-angled-trigonometry'" style="background-image: url('../../files/GT/NRAT/Nrat-small.jpg')" title="3.2 Non-right angled trigonometry"> </div> <div class="content"> <h4 class="head"><a href="../2261/32-non-right-angled-trigonometry.html">3.2 Non-right angled trigonometry</a></h4> <p class="body">Here we take trigonometry to the next level by working with triangles that do not have a right angle. We will work on three key rules. The Sine rule, the Cosine rule and the formula for th area of a triangle. All of these involve linking four...</p> </div> </div> <div class="item"> <div class="bg-cover cover-96" onclick="window.location='/mathsapplications/page/2196/33-applications-of-trigonometry'" style="background-image: url('../../images/compass.jpg')" title="3.3 Applications of trigonometry"> </div> <div class="content"> <h4 class="head"><a href="../2196/33-applications-of-trigonometry.html">3.3 Applications of trigonometry</a></h4> <p class="body">Given the focus on applications in this course, we will look more specifically at real world problems which trigonometry can help solve. Examples of this include bearings and angles of elevation/depression, which are likely to form a large...</p> </div> </div> <div class="item"> <div class="bg-cover cover-96" onclick="window.location='/mathsapplications/page/1862/34-circles'" style="background-image: url('../../circle.png')" title="3.4 Circles"> </div> <div class="content"> <h4 class="head"><a href="../1862/34-circles.html">3.4 Circles</a></h4> <p class="body">Circles In this section you will learn how to find the length of an arc of a circle and the area of a sector. Make sure you are confident rearranging formulae and solving equations before making a start on this page! Key Concepts In this unit...</p> </div> </div> <div class="item"> <div class="bg-cover cover-96" onclick="window.location='/mathsapplications/page/2120/35-36-perpendicular-bisectors-voronoi-diagrams-'" style="background-image: url('../../images/vornoi.png')" title=" 3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams "> </div> <div class="content"> <h4 class="head"><a href="../2120/35-36-perpendicular-bisectors-voronoi-diagrams-.html">3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams </a></h4> <p class="body">In this fascinating topic, we will delve into the wonderful world of Voronoi diagrams. This includes creating Voronoi diagrams with perpendicular bisectors, adding a new site, nearest neighbour interpolation and the toxic waste dump problem....</p> </div> </div> </div> <h2>Key Questions</h2> <p>The following are list of key questions that you might be asking about these topics with links to the places where you can get the answers!</p> <h2>How do we calculate with area and circumference of a circle? </h2> <p>There are some useful formulae to learn how to use to help you to do this: <a href="../1862/34-circles.html" title="3.4 Circles">3.4 Circles</a></p> <h2>How do you find the area of a sector and the length of an arc of a circle?</h2> <p>We can look at the fractions of the circle that we are trying to find in order to do this. <a href="../1862/34-circles.html" title="3.4 Circles">3.4 Circles</a></p> <h2>What are Voronoi diagrams used for? </h2> <p>Voronoi diagrams have a huge number of applications, from city planning, to architecture, to biological modelling. <a href="../2120/35-36-perpendicular-bisectors-voronoi-diagrams-.html" title=" 3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams "> 3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams </a></p> <h2>How can we find a missing angle or length of a right angled triangle?</h2> <p>Trigonometry can be used to find this. <a href="../2260/32-right-angled-trigonometry.html" title="3.2 Right angled Trigonometry">3.2 Right angled Trigonometry</a></p> <h2>How are volume and surface area calculated?</h2> <p>We can use various formulae to help us to find volume and surface area <a href="../2398/31-volume-and-surface-area.html" title="3.1 Volume and surface area">3.1 Volume and surface area</a></p> <h3> </h3> <hr class="thin"><div class="row"><div class="col-md-12"><br><ul class="resources"><li class="resource-item"><div class="img-container"><img class="thumb thumb-cover" src="../../files/GT/vsa/vsa.jpg"></div><div class="media-body"><h4 style="font-size: 19px;"><a class="text-normal" href="../2398/31-volume-and-surface-area.html">3.1 Volume and surface area</a></h4><p class="body">This section is all about the volume and surface area of prisms, cylinders, pyramids, cones and spheres! All of these shapes has their own unique properties and this section is about understanding and calculating the volumes and surface areas. </p></div></li><li class="resource-item"><div class="img-container"><img class="thumb thumb-cover" src="../../files/GT/RAT/Rat2-small.jpg"></div><div class="media-body"><h4 style="font-size: 19px;"><a class="text-normal" href="../2260/32-right-angled-trigonometry.html">3.2 Right angled Trigonometry</a></h4><p class="body">This part of trigonometry can be seen in the recurring relationships between the sides of right angles triangles. The relationship means that we can use two bits of information about a triangle to work out a third and so on until we know everything...</p></div></li><li class="resource-item"><div class="img-container"><img class="thumb thumb-cover" src="../../files/GT/NRAT/Nrat-small.jpg"></div><div class="media-body"><h4 style="font-size: 19px;"><a class="text-normal" href="../2261/32-non-right-angled-trigonometry.html">3.2 Non-right angled trigonometry</a></h4><p class="body">Here we take trigonometry to the next level by working with triangles that do not have a right angle. We will work on three key rules. The Sine rule, the Cosine rule and the formula for th area of a triangle. All of these involve linking four...</p></div></li><li class="resource-item"><div class="img-container"><img class="thumb thumb-cover" src="../../images/compass.jpg"></div><div class="media-body"><h4 style="font-size: 19px;"><a class="text-normal" href="../2196/33-applications-of-trigonometry.html">3.3 Applications of trigonometry</a></h4><p class="body">Given the focus on applications in this course, we will look more specifically at real world problems which trigonometry can help solve. Examples of this include bearings and angles of elevation/depression, which are likely to form a large...</p></div></li><li class="resource-item"><div class="img-container"><img class="thumb thumb-cover" src="../../circle.png"></div><div class="media-body"><h4 style="font-size: 19px;"><a class="text-normal" href="../1862/34-circles.html">3.4 Circles</a></h4><p class="body">Circles In this section you will learn how to find the length of an arc of a circle and the area of a sector. Keep track of your progress and practice the exam questions using this document: Check that you are confident learnin Can you round...</p></div></li><li class="resource-item"><div class="img-container"><img class="thumb thumb-cover" src="../../images/vornoi.png"></div><div class="media-body"><h4 style="font-size: 19px;"><a class="text-normal" href="../2120/35-36-perpendicular-bisectors-voronoi-diagrams-.html"> 3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams </a></h4><p class="body">In this fascinating topic, we will delve into the wonderful world of Voronoi diagrams. This includes creating Voronoi diagrams with perpendicular bisectors, adding a new site, nearest neighbour interpolation and the toxic waste dump problem....</p></div></li></ul></div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report 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