Scaling New Heights: Mastering Angle of Elevation and Depression
Lesson Description
Video Resource
Key Concepts
- Angle of Elevation
- Angle of Depression
- Trigonometric Ratios (Sine, Cosine, Tangent)
- Alternate Interior Angles
- Right Triangle Trigonometry
Learning Objectives
- Define and differentiate between angle of elevation and angle of depression.
- Draw accurate diagrams representing angle of elevation and depression problems.
- Apply trigonometric ratios (sine, cosine, tangent) to solve for unknown sides in right triangles related to angle of elevation and depression problems.
- Utilize the concept of alternate interior angles to solve related problems.
Educator Instructions
- Introduction (5 mins)
Begin by reviewing basic trigonometric ratios (SOH CAH TOA). Then, introduce the concepts of angle of elevation and angle of depression with clear definitions and visual aids. Show the video from 0:13-0:45. - Diagram Drawing (10 mins)
Emphasize the importance of drawing accurate diagrams. Explain the 'rectangle' method as a helpful strategy, as shown in the video from 0:45-1:26. Practice drawing diagrams based on various word problems. - Example Problem and Solution (15 mins)
Work through the example problem from the video (1:26-2:32) step-by-step, highlighting the use of the sine ratio. Encourage student participation in identifying the opposite and hypotenuse sides. Discuss the concept of alternate interior angles as shown in the video from 2:32 onward. - Practice Problems (15 mins)
Provide students with several practice problems involving angle of elevation and depression. Encourage them to work individually or in pairs, drawing diagrams and applying trigonometric ratios to find solutions. Circulate to provide assistance. - Review and Q&A (5 mins)
Review the key concepts and solutions to the practice problems. Address any remaining questions or concerns.
Interactive Exercises
- Diagram Drawing Challenge
Present students with complex word problems and challenge them to draw accurate diagrams within a set time limit. - Real-World Measurement
Use clinometers (or phone apps) to measure the angle of elevation to the top of a tall building or tree. Then, using the distance to the base, calculate the height of the object.
Discussion Questions
- How do angle of elevation and angle of depression differ?
- Why is it important to draw a diagram when solving these types of problems?
- How can the concept of alternate interior angles simplify problem-solving?
Skills Developed
- Problem-solving
- Critical thinking
- Spatial reasoning
- Application of trigonometric ratios
Multiple Choice Questions
Question 1:
The angle of elevation is measured from the ___________.
Correct Answer: Horizontal
Question 2:
The angle of depression is measured ___________.
Correct Answer: Down from the horizontal
Question 3:
Which trigonometric ratio relates the opposite side and hypotenuse of a right triangle?
Correct Answer: Sine
Question 4:
Alternate interior angles formed by parallel lines and a transversal are always ___________.
Correct Answer: Congruent
Question 5:
A ladder leaning against a wall forms an angle of elevation of 60 degrees with the ground. If the ladder is 12 feet long, how far up the wall does it reach?
Correct Answer: 10.4 feet
Question 6:
From the top of a cliff 50 meters high, the angle of depression to a boat is 30 degrees. How far is the boat from the base of the cliff?
Correct Answer: 50√3 meters
Question 7:
Which trigonometric function would you use to find the angle of elevation if you know the opposite and adjacent sides of the right triangle?
Correct Answer: Tangent
Question 8:
If the angle of elevation from point A to the top of a building is 45 degrees and the distance from point A to the base of the building is 20 feet, what is the height of the building?
Correct Answer: 20 feet
Question 9:
A bird is sitting on top of a 15-foot tree. If a person is standing 40 feet from the base of the tree, what is the angle of elevation from the person to the bird?
Correct Answer: arctan(15/40)
Question 10:
A kite is flying 20 feet above the ground and the string is 50 feet long. What is the angle of elevation of the string?
Correct Answer: arcsin(20/50)
Fill in the Blank Questions
Question 1:
The angle of __________ is the angle formed by looking up from the horizontal.
Correct Answer: elevation
Question 2:
The angle of __________ is the angle formed by looking down from the horizontal.
Correct Answer: depression
Question 3:
The trigonometric ratio that relates the opposite side to the adjacent side is __________.
Correct Answer: tangent
Question 4:
When parallel lines are cut by a transversal, __________ interior angles are congruent.
Correct Answer: alternate
Question 5:
If you know the angle of elevation and the length of the hypotenuse, you can use the __________ function to find the length of the opposite side.
Correct Answer: sine
Question 6:
The mnemonic __________ is a helpful way to remember the trigonometric ratios.
Correct Answer: SOH CAH TOA
Question 7:
When solving word problems with angles of elevation and depression, it is important to draw a(n) __________.
Correct Answer: diagram
Question 8:
From a point on the ground, the angle of elevation to the top of a flagpole is 30 degrees. If the point is 20 feet from the base of the flagpole, the height of the flagpole can be found using the __________ function.
Correct Answer: tangent
Question 9:
If the angle of depression from a hot air balloon to a person on the ground is 60 degrees, and the height of the balloon is known, the horizontal distance can be found by applying knowledge of __________ interior angles and trigonometric ratios.
Correct Answer: alternate
Question 10:
If the angle of elevation to the top of a tree is 45 degrees and you are 10 feet from the base of the tree, the height of the tree is __________ feet.
Correct Answer: 10
Educational Standards
Teaching Materials
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