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Course: High School Math with NAO
Law of Sine and Cosine

  • 9-12 grade
  • Intermediate

Lesson Description:

The students give the correct angle of Nao's elbow so Nao robot can take his hat off and perform a proper greeting by using the law of sine and cosines.


 

Standards Covered

CCSS.MATH.CONTENT.HSG.SRT.D.10

(+) Prove the Laws of Sines and Cosines and use them to solve problems.

CCSS.MATH.CONTENT.HSG.SRT.D.11

(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

CCSS.MATH.PRACTICE.MP4

Model with mathematics.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

image description

Lesson Modules


Teaching Tips:

Show the live demo of Nao robot to the students. 

  1. Charge NAO robot's battery the night before
  2. Turn on NAO robot by pressing the chest button. 
  3. Connect your robot to your computer by using its IP address in Choregraphe. 
  4. Place NAO in the middle of the class or in front so everyone can see the live demonstration.
  5. Use this hat so NAO can greet by taking the hat.
  6. Run this Choregraph file. 

Have students answer the question. Tell them they must enter their answer using only one word.  

See the live demo of Nao robot. 







What geometric shape should the arm represent in order for the robot to grab the hat? Type your answer using only ONE word.


Teaching Tips:

Have students investigate the challenge. 
The students can also recall the law of cosines with the interactive tool and apply it to the context.

Have students calculate the unknown value and add their findings to the question. 


You need to tell Nao robot how high he needs to reach his fingertips to grab the hat. Use Math to solve this challenge. 

 

 

Law of Sines

Click on the empty box next to Right Triangle and see how you can formulate the Law of Sines.


 

How Does Law of Sines Apply?

See how you can apply the Law of Sines to this context. 

 

 

Answer the following question.



Calculate how far Nao needs to move his fingers from his shoulder point to reach the brim of the hat? Type your answer using only a number.


Teaching Tips:

Have students investigate the challenge. 
The students can also recall the law of cosines with the interactive tool and apply it to the context.

Have students calculate the unknown value and add their finds to the poll question. 

Just like you used Law of Sines, this challenge is very similar but you need to use Law of Cosines since you have a SAS triangle. 

 

 

Law of Cosines

Recall how you can formulate the Law of Cosines.

 

 

How Does Law of Cosines Apply?

Apply the Law of Cosines to this context.

 



Answer the following question. 


Calculate how far Nao needs to move his fingers from his shoulder point to reach the brim of the hat. Type your answer using only a number.


Teaching Tips:

Have students investigate the challenge. 
The students can also recall the law of cosines with the interactive tool and apply it to the context.

Have students calculate the unknown value and add their findings to the question. 

In this case, you have an SSS triangle. You can use the Law of Cosines and the inverse cosines to find the angle.  

 

 

Arccosines (Inverse Cosines)


Type your answer only in one word. 


What is the elbow angle Nao needs to reach to the brim of the hat to greet properly? Type your answer using only a number in degree.


Teaching Tips:

Simulation

Have students play with the simulation to try out their answers.

Programming

Have students gather in groups of 2 or 3. Print out the hat materials and give them scissors and glue/tape. Students can decorate the hat as they wish but make sure the hat-making activity is limited (less than 10 minutes). 

Take a turn to run NAO robot. When you connect NAO to another computer, make sure you DISCONNECT first, otherwise, NAO will not be able to connect for 15 minutes. 

Show the class how to change the elbow angle in Choregraphe. 

Simulation

 

 

Programming

Open this file in your Choregraphe program. 

To make a change to the elbow angle, follow the instruction below. 


Teaching Tips:

Have students mark on the self-reporting scores on each concept. You will see the class data.
Have students write the in-depth questions. You have access to the answers from the dashboard.

If time is allowed, have a quick discussion with the students on what went well and what could have gone differently to make the learning better. Try to apply this feedback to the next lesson.

You helped Nao to greet properly like a real gentleman by using the law of sines and cosines. 

The law of sines can be used when you know two angles of a triangle (AAS) and the side length that is not between the angles. 

And the law of cosines can be used when you know two sides and an angle between (SAS). 

You also used an inverse cosine to calculate the angle when you have three sides (SSS).


Directions: Have quiet time individually to answer the following questions. Don't worry. Your response won't be graded. 

I understand the concept of law of sines & cosines and its application.
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you applied the law of sines or cosines for the given challenge in this lesson.

I understand the concept of inverse cosines.
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it



What is the coolest thing you learned today? Type your answer using only one word.