THINKING ABOUT OUR CHOICES (FREE) Solve the triangle using the Pythagorean Formula 1.How many given sides do you need to solve the missing side of the

THINKING ABOUT OUR CHOICES (FREE)Solve the triangle using the

Pythagorean Formula

1. How many given sides do you need to solve the missing side of the triangle?

2. Does the Pythagorean Formula help you solve the other parts of the triangle aside from the unknown sides? Expound your answer.

Find the vertices of the triangle and use the Distance Formula to solve the given

triangle

1. Are the vertices always available? If available, how do you use the Distance Formula?

2. Does the Distance Formula solve the angles of the given triangle? Why?

Use trigonometric functions to solve the given triangle

1. Given an acute angle and a side, how will you solve the given triangle?

2. Do you think this choice will solve the given triangle completely? Why?

Use the measuring instruments to solve the given triangle.

1. What are the instruments that you may use in solving the given triangle?

2. Why do you think using the instrument will solve your task easily?

WORKSHEET #1 Name: __________________________ Yr. & Section: _____

Reflections:1. How will you compare the method you chose to that of your classmates’? ____________________________________________________________________________ 2. Do you think your choice is the best approach to solve the triangle? Explain your answer. ___________________________________________________________________ 3. How did you learn from one another? ____________________________________________________________ 4. Next time you encounter this kind of problem how prepared are you to deal with it? _________________________________________________________________


How far can you go?

Browse the given website and/or read the references available to help you define the following terms:

1. opposite sides -

2. adjacent sides -

3. hypotenuse -

4. sine -

5. cosine –

6. tangent -


LESSON 1:

Given the measure of an acute angle of a triangle and the length of its opposite side. Solve the missing parts of the given triangle. Use the references in the math basket to be able to solve activity 1

ACTIVITY 1

T

a

n

A t N Given: Rt. TAN, where A is right, N = 40

and n = 12 cm. Find: T, a and t.

You can use the trigonometric table or calculator to solve the succeeding word problems. You are provided with guide questions to facilitate you in doing your tasks.OK! Start moving and enjoy the fun of solving right triangles.


Using the given parts of the triangle, what trigonometric functions will you use to determine the length of side a? __________ side t?

After you verify the functions, which operation is easier to use?

What theorem in Geometry will you use to find the other acute angles?

When will you apply the Pythagorean formula in solving the right triangle?


LESSON 2:

Given two sides of a triangle solve the missing parts of the given triangle. Use the references in the math basket to facilitate you in solving the problem.

ACTIVITY 2

Use rt. TAN, where a = 17 cm and n = 13 cm. Solve the missing parts of TAN.

• What possible solution can you think of to solve side t? ___________________________________________________________________________________________________________________________________________________________________________________________________

2. Show the possible solutions to solve the acute angles and explain which is the easier method?

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


How would you apply what you have learned in Lessons 1 and 2?

Your friend is waving at you at the window of a 10-storey building, 100 meters above the ground. The angle of depression where your friend stands is 36O. How far are you from your friend?

What factors will you consider to help you find the answer?


MIND MAP

Solution of Right Triangles

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6

How will you solve the problem?Write the steps that you can think of to

solve the word problem!


Working with Right Triangles

Activity 3: Apply what you learned in solving right triangles in the given problem. Analyze the problem carefully.

A ladder leans against a building. The foot of the ladder is 6 feet from the building. The ladder reaches height of 14 feet on the building. How long is the ladder? What angle does the ladder form to the building at the height of 14 ft?


Criteria Remarkable Capable Learner Neophyte Student’sRating

Teacher’s Rating

MathematicalKnowledge(8 points)

Portrays in-depth understanding of the relevant concepts and/or processes.(7-8)

Displays complete most important components of the task.(5-6)

Lacks clear understanding of the problem.(3-4)

Shows little understanding or none at all of the problem.(1-2)

Strategies(6 points)

Uses clear evidence of a solution process that is complete and systematic(6)

Uses representation that clearly depict the problem(4-5)

Applies some some appropriate procedures.(2-3)

Applies incorrect or irrelevant procedures.(1)

Problem Solving(6 points)

Show evidence of insightful thinking to explore the problem.(6)

Skills and strategies havesome focus, but clarity is limited.(4-5)

Fails to see alternative solutions that the problem requires.(2-3)

Does not try to do the assigned task(1)

Quality of Work(5 points)

Provides work of the highest quality(5)

Provides high quality work.(4)

Provides work that occasionally needs to be revised.(2-3)

Provides work that usually needs to be revised.(1)

Working with Others(5 points)

Almost always listens to, shares with, and supports the efforts of others. Tries to keep people working well together.(5)

Usually listens to, shares, with, and supports the efforts of others. Does not cause "waves" in the group. (4)

Often listens to, shares with, and supports the efforts of others, but sometimes is not a good team member. (2-3)

Rarely listens to, shares with, and supports the efforts of others. Often is not a good team player.(1)

Total Score

RUBRIC Name: __________________________ Yr. & Section: _____

Documents

THINKING ABOUT OUR CHOICES (FREE) Solve the triangle using the Pythagorean Formula 1.How many given sides do you need to solve the missing side of the