 Standard #: MAFS.912.G-SRT.3.8

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Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Cluster: Define trigonometric ratios and solve problems involving right triangles. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

TEST ITEM SPECIFICATIONS

Item Type(s): This benchmark may be assessed using: EE item(s)
Also assesses:

MAFS.912.G-SRT.3.6

MAFS.912.G-SRT.3.7

Assessment Limits :
Items will assess only sine, cosine, and tangent to determine the
length of a side or an angle measure.
Calculator :

Neutral

Clarification :
Students will use trigonometric ratios and the Pythagorean theorem
to solve right triangles in applied problems.

Students will use similarity to explain the definition of trigonometric
ratios for acute angles.

Students will explain the relationship between sine and cosine of
complementary angles.

Students will use the relationship between sine and cosine of
complementary angles.

Stimulus Attributes :
For G-SRT.3.8, items must be set in a real-world context.

For G-SRT.3.6 and G-SRT.3.7, items must be set in a mathematical
context.

For G-SRT.3.8, items may require the student to apply the basic
modeling cycle.

Response Attributes :
Items may require the student to find equivalent ratios.

Items may require the student to use or choose the correct unit of
measure.

Multiple-choice options may be written as a trigonometric equation.

Equation Editor items may require the student to use the inverse
trigonometric function to write an expression.

SAMPLE TEST ITEMS (1)

 Test Item # Question Difficulty Type Sample Item 1 In the 1990s, engineers restored the building so that angle y changed from 5.5º to 3.99º.To the nearest hundredth of a meter, how much did the restoration change the height of the Leaning Tower of Pisa? N/A EE: Equation Editor

Related Courses

 Course Number1111 Course Title222 1200400: Intensive Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1202340: Pre-Calculus (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1211300: Trigonometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7912065: Access Geometry (Specifically in versions: 2015 and beyond (current))

Access Point

 Access Point Number Access Point Title MAFS.912.G-SRT.3.AP.8a Apply both trigonometric ratios and Pythagorean Theorem to solve application problems involving right triangles.

Original Student Tutorial

 Name Description Around the World with Right Triangles Learn how to use trigonometric ratios to solve a real-world application. There are many famous monuments across the world. The measurements of these monuments were often found using trigonometric ratios. Today, there are devices that use laser beams to measure distances and heights, but trigonometric ratios are still widely used.

Tutorial

 Name Description Basic Trigonometry This tutorial gives an introduction to trigonometry. This resource discusses the three basic trigonometry functions, sine, cosine, and tangent. LSSS Tutorial: Introduction to Vectors and Scalars This resource is intended to serve as a concise introduction to vector and scalar quantities for teachers of secondary math and science. It provides definitions of vectors and scalars as well as physical examples of each type of quantity, and also illustrates the differences between these two types of quantities in both one and two dimensions, through determinations of both distance (scalar) and displacement (vector). Projectile at an angle This video discusses how to figure out the horizontal displacement for a projectile launched at an angle. Using Trigonometry to solve for missing information This tutorial will show students how to use trigonometry to solve for missing information in right triangles. This video shows worked examples using trigonometric ratios to solve for missing information and evaluate other trigonometric ratios.

Virtual Manipulative

 Name Description Demonstrate the Pythagorean Theorem Representation to illustrate the Pythagorean Theorem. Pythagorean Theorem Manipulatives This web address, from the National Library of Virtual Manipulatives, will help teachers and students validate the Pythagorean Theorem both geometrically and algebraically. It can be used interactively with the Smartboard and the Promethean Board to create a better understanding of the topic. Right Triangle Solver This virtual manipulative will help the students in understanding that the relationships found in right triangles can be used to solve many applied problems in science and engineering. The right triangle solver manipulative displays a triangle with some its sides and angles given. The student is then asked to determine values of the remaining sides and angles by choosing a workable strategy. Triangle Solver The triangle solver manipulative displays a triangle with some of its sides and angles given. The students are then asked to determine values of the remaining sides and angles. Students are motivated to choose a workable strategy such as using the Pythagorean theorem, the sine, cosine, tangent relationships, the law of sines, or the law of cosines. They are directed through the key steps of the chosen strategy to find the unknown sides and the angles.

Formative Assessment

 Name Description Holiday Lights Students are asked to solve a problem in a real world context requiring the use of the Pythagorean Theorem. Lighthouse Keeper Students are asked to find the difference between two lengths in a real world context requiring right triangle trigonometry. Perilous Plunge Students are asked to find an unknown length in a real world context requiring right triangle trigonometry. River Width Students are asked to find an unknown length in a real world context requiring right triangle trigonometry. Step Up Students are asked to explain the relationship among angles in a diagram involving a right triangle and to find one angle of the right triangle. TV Size Students are asked to solve a problem in a real world context requiring the use of the Pythagorean Theorem. Washington Monument Students are asked to find the angle of elevation in a real world situation modeled by a right triangle. Will It Fit? Students are asked to solve a problem in a real world context using the Pythagorean Theorem.

Teaching Idea

 Name Description Measuring the Distance to Nearby Stars Using Parallax This video provides a very complete and detailed overview of the parallax effect and how it can be used to measure astronomical distances using the tangent function. A number of student activities are presented throughout the 26 minute video, so students can have the opportunity to engage in measuring distances to stars and other local landmarks and can try making the required calculations on their own.The relevance of this concept to other fields, such as surveying, is also noted in the video.

Video/Audio/Animation

 Name Description MIT BLOSSOMS - The Juice Seller’s Problem "This video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangle's area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases. Materials necessary include: equilateral containers of equal heights; sand; and measuring devices. Examples of in-class activities for the breaks between video segments include class discussions, individual calculations and small group problem solving." (from MIT Blossoms' "Pythagoras and the Juice Seller")

Perspectives Video: Expert

 Name Description Oceanography & Math A discussion describing ocean currents studied by a physical oceanographer does and how math is involved.

Assessment

 Name Description Sample 1 - High School Geometry State Interim Assessment This is a State Interim Assessment for 9th-12th grade. Sample 2 - High School Geometry State Interim Assessment This is a State Interim Assessment for 9th-12th grade. Sample 3 - High School Geometry State Interim Assessment This is a State Interim Assessment for 9th-12th grade. Sample 4 - High School Geometry State Interim Assessment This is a State Interim Assessment for 9th-12th grades.

Lesson Study Resource Kit

 Name Description The Motion of Objects This 9-12 Lesson study resource kit is designed to engage teachers of physical science and physics in the planning and design of an instructional unit and research lesson pertaining to the motion of objects. Included in this resource kit are unit plans, concept progressions, formative and summative assessments, complex informational texts, and etc. that align to relevant NGSSS science, and the new Florida standards for mathematics and English language arts.