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Things Are Looking Up!

Things Are Looking Up!. Objective: Indirect Measurement of Height Using Right Triangles Prerequisite skills: Trig D efinitions Solve Trig Equations Tools: Clinometer Measuring Tape Calculators. CA Standards (18.0 & 19.0):

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Things Are Looking Up!

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  1. Things Are Looking Up! Objective: Indirect Measurement of Height Using Right Triangles Prerequisite skills: Trig Definitions Solve Trig Equations Tools: Clinometer Measuring Tape Calculators

  2. 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.

  3. Mt. Everest • What do you know about this mountain? • Estimate the height of Mt. Everest . • What word represents height in terms of a mountain?

  4. 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?

  5. Let’s Consider…… • A Mountain with Vertical Height Mt. Rushmore National MonumentBlack Hills, South DakotaCompleted in 1941

  6. Estimate the Elevation.

  7. How Do I Use Trigonometry for Indirect Measurement? • Write any observations made from the picture. Draw a sketch if needed.

  8. 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 Eye Height Distance to Object

  9. Indirect MeasurementReflection Explain how trigonometry is used for indirect measurement of height. Consider the following: • Measurements that are Needed • Visual Representation • Proper Use of Vocabulary

  10. 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

  11. Making Your Own Clinometer • Template • Protractor

  12. Using Your Clinometer • Line of Sight to Object • Angle Measures: From Horizontal Eye Height • Partner Practice: Ceiling & Floor

  13. Clinometer Activity Task: Use indirect measurement to find the height of two tall objects • Materials: Tape Measure, Clinometer, Calculator

  14. 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 reasonableheights.

  15. 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

  16. 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?

  17. 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?

  18. Viewing Mt. Rushmore • Distance of Sightseer to base of Mountain (as taken from picture): • Eye Height of Sightseer: • Clinometer Reading: 729 feet 5’7” • Find the height of • Mt. Rushmore from the Avenue of Flags pathway.

  19. Mt Rushmore Elevation 5725 feet • Is height the same as elevation? Explain.

  20. Viewing Mt. Rushmore Find the elevation of the Avenue of Flags pathway.

  21. 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 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.

  22. Mt. Everest Elevation 29,035 feet

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