4.11.6 Angles of Elevation and Depression
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This document defines and provides examples of angles of elevation and depression. It explains that an angle of elevation is formed between a horizontal line and a line of sight to a point above the line, while an angle of depression is formed between a horizontal line and a line of sight to a point below the line. The document also shows how to identify these angles and solve problems involving them using trigonometric functions like tangent.
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Angle of elevation and depression by: Erwin Navarro
This document discusses measuring angles of elevation and depression using trigonometric ratios. It provides examples of how to calculate missing lengths or angles using trig functions when given the angle of elevation or depression and one leg of the right triangle formed by the observer's line of sight. Key terms like line of sight, angle of elevation, and angle of depression are defined. Steps for solving problems are outlined along with sample problems and solutions.
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This document outlines an activity to help students understand the concepts of angle of elevation and angle of depression. The activity involves students finding classmates at their eye level or taller/shorter, then illustrating tall and short objects outside. They are expected to differentiate elevation and depression angles, link them to real-life contexts, and illustrate the concepts. Key terms like line of sight, elevation angle, and depression angle are defined. Examples are given and students must identify these angles in diagrams. Finally, a math problem applies the elevation angle concept.
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This document provides a strategic intervention material to help students learn about solving real-life problems involving right triangles using trigonometric ratios. It begins with definitions of key terms like line of sight, angle of elevation, and angle of depression. Students are given examples of problems involving these angles and their solutions. Later activities require students to illustrate problem situations, identify given information, formulas used, and solve problems determining unknown angles or distances. The material aims to supplement classroom learning and help students independently practice and understand solving right triangle problems.
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This document discusses angles of elevation and depression. It defines an angle of elevation as the angle formed between a horizontal line and the line of sight to an object located above the horizontal line. An angle of depression is defined as the angle formed between a horizontal line and the line of sight to an object located below the horizontal line. The document provides examples of solving problems involving angles of elevation and depression using trigonometric functions like tangent, sine, and the Pythagorean theorem. It emphasizes drawing a diagram, identifying if it is an angle of elevation or depression, and using the appropriate trigonometric ratio to solve for missing lengths.
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This document defines the angle of depression as the angle below the horizontal that an observer looks to see an object lower than them, and defines the angle of elevation as the angle above the horizontal an observer looks to see a higher object. It provides two examples using trigonometry: one calculating the height of a tree using a 51 degree angle of elevation, and another calculating the distance to a boat using a 10 degree angle of depression.
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This document discusses measuring angles of elevation and depression using trigonometric ratios. It provides examples of how to calculate missing lengths or angles using trig functions when given the angle of elevation or depression and one leg of the right triangle formed by the observer's line of sight. Key terms like line of sight, angle of elevation, and angle of depression are defined. Steps for solving problems are outlined along with sample problems and solutions.
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This document outlines an activity to help students understand the concepts of angle of elevation and angle of depression. The activity involves students finding classmates at their eye level or taller/shorter, then illustrating tall and short objects outside. They are expected to differentiate elevation and depression angles, link them to real-life contexts, and illustrate the concepts. Key terms like line of sight, elevation angle, and depression angle are defined. Examples are given and students must identify these angles in diagrams. Finally, a math problem applies the elevation angle concept.
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This document discusses angles of elevation and depression. It defines an angle of elevation as the angle formed between a horizontal line and the line of sight to an object located above the horizontal line. An angle of depression is defined as the angle formed between a horizontal line and the line of sight to an object located below the horizontal line. The document provides examples of solving problems involving angles of elevation and depression using trigonometric functions like tangent, sine, and the Pythagorean theorem. It emphasizes drawing a diagram, identifying if it is an angle of elevation or depression, and using the appropriate trigonometric ratio to solve for missing lengths.
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This document defines the angle of depression as the angle below the horizontal that an observer looks to see an object lower than them, and defines the angle of elevation as the angle above the horizontal an observer looks to see a higher object. It provides two examples using trigonometry: one calculating the height of a tree using a 51 degree angle of elevation, and another calculating the distance to a boat using a 10 degree angle of depression.
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This document discusses angles of elevation and depression. It defines an angle of elevation as formed between a horizontal line and the line of sight to a point above the line, while an angle of depression is formed between a horizontal line and the line of sight to a point below the line. It provides examples of how to identify if an angle is elevation or depression and how to solve problems involving these angles using trigonometric functions like tangent.
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Here are the steps to solve this problem using trigonometry:
1. Draw a sketch of the situation showing the hot air balloon, observer, and relevant angles and distances.
2. Label the given information: The observer is 20 m from the base of the balloon and the angle of elevation is 35°.
3. Identify the trigonometric ratio to use based on the given and missing information. Since we are given an angle of elevation and the distance from the observer to the base of the balloon, we will use tangent.
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Tan 35° = Opposite/Adjacent
Tan 35° = Height/20
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Even and off functions basic presentation with questions 2
Here are the answers to your questions:
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12. To determine if a function is even, odd, or neither from its equation, I analyze the exponents of x. An even function will have only even exponents of x, an odd function will have only odd exponents of x, and a function with a mix of even and odd exponents is neither.
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angle of depression and angle of elevation
angle of depression and angle of elevation
angle of depression and angle of elevation
angle of depression and angle of elevation
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4.11.6 Angles of Elevation and Depression
- 1. 4.11.6 Elevation and Depression The student is able to (I can): • Solve problems involving angles of depression or elevation
- 2. angle of elevation This is an angle formed by a horizontal line and the line of sight to a point aboveaboveaboveabove the line. angle On the SAT, this is called the angle of inclination.
- 3. angle of depression This is an angle formed by a horizontal line and a line of sight to a point belowbelowbelowbelow the line. angle On the SAT, this is called the angle of declination.
- 4. These two angles are related because the horizontal lines are parallel: To identify whether an angle is an angle of elevation or depression, check whether the line of sight is above or below the horizontal line.
- 5. Identify whether the angle is an angle of elevation or depression. 1. ∠1 2. ∠2 3. ∠3 4. ∠4 depression depression elevation elevation
- 6. Examples 1. If a tree casts a shadow 18 feet long when the sun is at an elevation of 35˚, how tall is the tree to the nearest foot? 35˚ 18´ (adj) x (opp) x tan35 18 ° = x = 13 feet = °x 18tan35
- 7. 2. A plane, at an altitude of 3000 feet, observes the airport at an angle of 27˚. What is the horizontal distance between the plane and the airport to the nearest foot? 27˚ 3000´ (opp) (27˚) x (adj) 3000 tan27 x ° = x = 5888 feet = ° 3000 x tan27