Goals: Each student will use trigonometric ratios to find angles of elevation and depression.
Objectives:
State Standards: MA.912.T.2.2 Solve real-world problems involving right triangles using technology when appropriate.
Engage: There is a ramp at school that students walk up each day to go through the door that leads into the building. There is also a staircase that most students use throughout the day. I will ask the students how steep they think the ramp and staircase are. I will ask them if they think the angles of elevation are within reason.
Lesson Procedure:
1) Students must review the trigonometric ratios using the mnemonic SOHCAHTOA
Sin = Opp Cos = Adj Tan = Opp
Hyp Hyp Adj
2) Draw figure on board. Explain to students that this represents our gymnasium and balcony. If someone is standing on the gym floor and looks up to someone on the balcony, an angle of elevation is formed. If someone is on the balcony and looks down to someone on the floor, an angle of depression is formed. If the two people are looking at one another, the two angles are congruent. Why? Because they are alternate interior angles.
3) Work through these three examples on the board.
Ex. 1 A TV tower stands 450 feet tall. There are several guywires attached to the tower. One of them forms an angle of elevation with the ground that is 58. How long is the guywire?
Ex. 2 The Empire State Building is approximately 1450 feet tall. If a person at the top of the building looks down at an angle of depression of 63◦ to see a taxicab, how far away is the taxicab from the base of the building?
Ex. 3 A ramp is 120 feet long and rises vertically 15 feet. What is the angle of elevation of the ramp?
Closure: This lesson should take two class periods. Students will be placed in groups of 3 and given a worksheet that lists different areas on campus that need to be measured. One student in each group will need to download Simply Angle app to their phone. Students will return to class to complete worksheet.
Extension/Elaboration: Once the angles have been determined, students could compare their findings to the ADA guidelines for ramp safety to make sure the ramps at school are in compliance.
Final Evaluation/Assessment: Students will use google docs to create a presentation of the concepts learned in this unit to share with classmates as a review for the final summative unit test. Students will include examples from each lesson. See example below and grading rubric.
Sample presentation
Grading Rubric
Objectives:
- With the aid of the app, Simply Angle (link at bottom of page), that student will need to download, the student will be able use angles of elevation and depression to find heights of objects located at school using trigonometric ratios.
State Standards: MA.912.T.2.2 Solve real-world problems involving right triangles using technology when appropriate.
Engage: There is a ramp at school that students walk up each day to go through the door that leads into the building. There is also a staircase that most students use throughout the day. I will ask the students how steep they think the ramp and staircase are. I will ask them if they think the angles of elevation are within reason.
Lesson Procedure:
1) Students must review the trigonometric ratios using the mnemonic SOHCAHTOA
Sin = Opp Cos = Adj Tan = Opp
Hyp Hyp Adj
2) Draw figure on board. Explain to students that this represents our gymnasium and balcony. If someone is standing on the gym floor and looks up to someone on the balcony, an angle of elevation is formed. If someone is on the balcony and looks down to someone on the floor, an angle of depression is formed. If the two people are looking at one another, the two angles are congruent. Why? Because they are alternate interior angles.
3) Work through these three examples on the board.
Ex. 1 A TV tower stands 450 feet tall. There are several guywires attached to the tower. One of them forms an angle of elevation with the ground that is 58. How long is the guywire?
Ex. 2 The Empire State Building is approximately 1450 feet tall. If a person at the top of the building looks down at an angle of depression of 63◦ to see a taxicab, how far away is the taxicab from the base of the building?
Ex. 3 A ramp is 120 feet long and rises vertically 15 feet. What is the angle of elevation of the ramp?
Closure: This lesson should take two class periods. Students will be placed in groups of 3 and given a worksheet that lists different areas on campus that need to be measured. One student in each group will need to download Simply Angle app to their phone. Students will return to class to complete worksheet.
Extension/Elaboration: Once the angles have been determined, students could compare their findings to the ADA guidelines for ramp safety to make sure the ramps at school are in compliance.
Final Evaluation/Assessment: Students will use google docs to create a presentation of the concepts learned in this unit to share with classmates as a review for the final summative unit test. Students will include examples from each lesson. See example below and grading rubric.
Sample presentation
Grading Rubric