* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download How Tall is This?
Survey
Document related concepts
Transcript
Things Are Looking Up! Objective: Indirect Measurement of Height Using Right Triangles Prerequisite skills: Trig Definitions Solve Trig Equations Tools: Clinometer Measuring Tape Calculators • CA Standards (18.0 & 19.0): Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side • Core Geometry G-SRT (6 & 7): Define trigonometric ratios and solve problems involving right triangles. • Core Math Practices MP.1 - Make sense of problems and persevere in solving them. MP.4 - Model with mathematics. MP.5 - Use appropriate tools strategically. MP.6 - Attend to precision. Mt. Everest • What do you know about this mountain? • Estimate the height of Mt. Everest . • What word represents height in terms of a mountain? Mt. Everest History • On May 29th 1953, Sir Edmund Hilary and his guide Tenzing Norgay were the first people to ascend to the peak of Mt. Everest, the highest elevation in the world. • How do you think Mt. Everest’s elevation was calculated? Let’s Consider…… • A Mountain with Vertical Height Mt. Rushmore National Monument Black Hills, South Dakota Completed in 1941 Estimate the Elevation. How Do I Use Trigonometry for Indirect Measurement? • Write any observations made from the picture. Draw a sketch if needed. How Do I Find the Height of Tall Objects Using Trigonometry? • What measurements are needed? • How would I calculate the tall object’s height? Height 𝒙° Eye Height Distance to Object Indirect Measurement Reflection Explain how trigonometry is used for indirect measurement of height. Consider the following: • Measurements that are Needed • Visual Representation • Proper Use of Vocabulary Act 2: Experiencing Indirect Measurement • Clinometer: An instrument used by surveyors in order to measure an angle of elevation or depression Measures Slope Angle From Horizontal Line Making Your Own Clinometer • Template • Protractor Using Your Clinometer • Line of Sight to Object • Angle Measures: From Horizontal Eye Height Partner Practice: Ceiling & Floor Clinometer Activity Task: Use indirect measurement to find the height of two tall objects Materials: Tape Measure, Clinometer, Calculator Clinometer Activity For each object: • Collect Three Data Sets: Use Different Distances to object • Draw a diagram with indicated measurements • Show all calculations that lead to object height include appropriate units • Check for reasonable heights. Clinometer Activity: Group Roles Surveyor: Operates Clinometer Supervises group to stay on task, time keep Technician: Reads Clinometer angle value Ensures accuracy of all measurements Specialist: Measures all distances with tape ruler Encourages team work Recorder: Writes down all data Manages tools for appropriate use Clinometer Activity Summary • Describe the mathematics required to indirectly measure a tall object’s height. • Explain any difficulties that may have arisen in order to complete the task. • How could we use our Clinometer Activity experience to calculate a mountain’s elevation? Act 3: Viewing Mt. Rushmore A sightseer is on the Avenue of Flags pathway. • What information or resources are needed for the sightseer to calculate the height of Mt. Rushmore from this pathway? Viewing Mt. Rushmore • Distance of Sightseer to base of Mountain (as taken from picture): 729 feet • Eye Height of Sightseer: • Clinometer Reading: 5’7” 𝟔𝟐. 𝟑𝒐 Find the height of Mt. Rushmore from the Avenue of Flags pathway. Mt Rushmore Elevation 5725 feet • Is height the same as elevation? Explain. Viewing Mt. Rushmore Find the elevation of the Avenue of Flags pathway. Act 4: Revisiting Mt. Everest Before climbing Mt. Everest, Sir Edmund Hillary and guide Tensing Norgay wanted to know its vertical height. At the base of the mountain, Hillary and Norgay measured a 𝟕𝟗. 𝟔𝟗𝟑𝟒° angle of elevation to the peak. They were 1 mile away from the altitude. • Draw a picture to represent their position with respect to the peak. • Find the elevation of Mount Everest. Mt. Everest Elevation 29,035 feet