Folio task trigonometry
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This document outlines a task for students to use trigonometry to determine the heights of various landmarks at Westminster School. Students will use a clinometer to measure the angle of elevation and distance to landmarks like the chapel, oval trees, and goal posts. Through right-angled triangle trigonometry and these measurements, students can calculate the approximate heights. The purpose is to apply mathematical concepts like trigonometry and communicate the results. Students must introduce the problem, method, apply the method by collecting data, showing work, analyzing results, and stating conclusions.
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Folio task trigonometry
- 1. Folio Task How tall is the ? Scenario You have been given the task to determine the approximate height of several Westminster School landmarks, for example the Chapel, the MMC, the oval gum trees, the SSC, the oval goal posts, the flag poles You will do this by measuring: the angle of elevation to the top of the object with your clinometer the ground distance from the clinometer to the base of the object (where possible) the distance from the clinometer to the ground Through the use of right-angled triangle trigonometry, you should then be able to find the approximate height of your chosen Westminster landmark. Materials required: Clinometer, measuring tape Purpose To demonstrate your ability to: accurately apply the mathematical concepts and relationships that you have learned in class to explore a mathematical model for the given data communicate your results and solutions. A completed investigation should include: an introduction that outlines the problem to be explored, including its significance, its features, and the context the method required to find a solution, in terms of the mathematical model or strategy to be used the appropriate application of the mathematical model or strategy, including o the generation or collection of relevant data and/or information, with details of the process of collection o mathematical calculations and results, and appropriate representations o the analysis and interpretation of results o reference to the limitations of the original problem a statement of the results and conclusions in the context of the original problem
- 2. Task One There is a problem with the Cloister!!!! It is apparently not a rectangle and the builders have made a mistake. Mr Bousfield has said, THE CLOISTERS IS A RECTANGLE and my Year 9 students will prove it. Using Pythagorass Theorem, determine if Mr Bousfield is correct. Task Two Choose a landmark where the perpendicular base is easily accessible and the actual height can be measured with a tape measure. We will choose the protective handrail of the upstairs cloisters. From two different points, measure the angle of elevation to the top of your chosen landmark and the horizontal distance to the foot of your chosen landmark. Using these measurements, calculate the height of your chosen landmark. Determine the average of your two results. Record your results in the table below. Object Angle of elevation Reading 1 Distance to object Reading 1 Angle of elevation Reading 2 Distance to object Reading 2 Compare your result with the result obtained by using the measuring tape. Calculate the difference between your answer and the correct answer and convert your answer to a percentage error Hint: % = %
- 3. Task Three Choose a landmark where the perpendicular base is easily accessible. From two different points, measure the angle of elevation to the top of your chosen landmark and the horizontal distance to the foot of your chosen landmark. Using these measurements, calculate the height of your chosen landmark. Record your results in the table below. Object Angle of elevation Reading 1 Distance to object Reading 1 Angle of elevation Reading 2 Distance to object Reading 2