#HemetLearnsTogether

Geometry Enrichment for the Week of 5/4/20 Dear Parents, Guardians and Students:   At HUSD the safety and education of our students is of highest importance. This packet of elected work in math has been developed to support your child in practicing and sharpening previously learned skills that will have a lasting impact on their education. Each week you will be provided with an optional packet of work to complete in your free time at home. For the most up to date information, check hemetusd.org. Thank you for continuing to trust us in your child’s education. It is our pleasure to continue to support you, and your child, during this challenging time. #HemetLearnsTogether Sincerely, ~HUSD Instructional Support Math Team  

This Week’s Writing Prompt:  

Given a right triangle with the following trigonometric ratio:  find all of the trigonometric ratios for this triangle.in(30 )s o = 2

1 How do you know these values are always going to be true when given this angle?

Games to play at home ● Checkers/Chess ● Battleship ● Blink ● Dominoes ● Uno/Crazy 8’s

● Monopoly ● Ticket to Ride ● Catan ● Cranium ● Sudoku

Skills to Practice Daily at Home: ❏ Addition and subtraction integers ❏ Pythagorean Theorem ❏ Computations with fractions ❏ Supplementary and complementary angles

 

Topics Covered in this week’s work: This Week’s Puzzle: 

 

❏ Finding the missing lengths, or angles, of a triangle

❏ Trigonometric ratios: sine, cosine and tangent

Family Challenge: Share with your family tonight:  ● What is one thing that you learned in math                 

today?  

● What is one thing that you wished you were                 able to know about your math work today? 

 

Task materials provided by Silicon Valley Math Initiative (SVMI), and Math Vision Project (MVP), for more information visit https://www.mathematicsvisionproject.org/

#HemetLearnsTogether

Task materials provided by Silicon Valley Math Initiative (SVMI), and Math Vision Project (MVP), for more information visit https://www.mathematicsvisionproject.org/

© SVMI 2018. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative info@svmimac.org

Locating a Drone Rubric The core elements of performance required by this task are: High School Geometry Similarity, Right Triangles, and Trigonometry G-SRT Define trigonometric ratios and solve problems involving right triangles 6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Modeling with Geometry G-MG Apply geometric concepts in modeling situations 1. Use geometric shapes, their measures, and their properties to describe objects 3. Apply geometric methods to solve design problems. Based on these, credit for specific aspects of performance should be assigned as follows:

Points

SectionPoints

1. Correctly labels the acute angles as: 30º and 60º 1 1

2. Gives a correct answer: 16√3 km (accept 27.7 km)

Shows a correct method such as:

The 30-60-90 angle theorem indicates the shortest leg is half the hypotenuse and that leg opposite 60º is the shortest side times the square root of three, thus 32√3/2

1

1

2

3. Draws the new location of the drone, then indicates that the altitude is equal to the horizontal leg or labels the acute angles each as 45º.

1

1

4. Gives a correct answer: 16 km and shows a correct method such as:

The short leg of the 30-60-90 triangle is 32/2 or 16 km. It is also the leg of the 45-45-90 triangle. Both legs are equal in a 45-45-90 right triangle, so the altitude is 16 km.

1

1

5. Gives a correct answer: the first radar dish is closer and gives a correct explanation such as: The angle of 36º is smaller than the angle of 45º, therefore slope of a 45º angle is steeper than a 36º angle. Since the rise of the two slopes are equal (both 16 km), therefore run of the 36º angle would have to be longer making the second dish farther away from the secure location.

1

1

6 Gives a correct answer: 22 km

Shows a correct method such as:

Tan 36º = 16/x, x = 16/.7265

1ft

1

2

Total Points 8

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45º

to d

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5.

Whi

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re c

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r to

the

dron

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____

____

____

____

____

____

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Expl

ain

how

you

kno

w.

____

____

____

____

____

____

____

____

____

____

____

____

____

____

____

____

____

____

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____

____

____

___

____

____

____

____

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____

____

____

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____

____

____

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6.

H

ow fa

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ay is

the

secu

re a

rea

from

the

seco

nd ra

dar d

ish?

___

____

____

____

____

____

km

Sh

ow h

ow y

ou fi

gure

d it

out.