Download MAFS.912.G-SRT.3.6 - Understand that by similarity, side ratios in

Standard #: MAFS.912.G-SRT.3.6
This document was generated on CPALMS - www.cpalms.org
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.
Subject Area: Mathematics
Grade: 912
Domain: Geometry: Similarity, Right Triangles, & Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles - Geometry - Major Cluster
Date Adopted or Revised: 02/14
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.
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved
Related Courses
Course Number
1206310:
1206315:
1206320:
7912065:
1200400:
Course Title
Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
Geometry Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
Access Geometry (Specifically in versions: 2015 and beyond (current))
Intensive Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
Related Access Points
Access Point
Access Points Number
MAFS.912.G-SRT.3.AP.6a:
Access Points Title
Using a corresponding angle of similar right triangles, show that the relationships of the side ratios are the same, which
leads to the definition of trigonometric ratios for acute angles.
Related Resources
Lesson Plan
Name
Calculating the Earth-Sun
distance using Satellite
Observations of a Venus
Transit:
Discovering Trigonometric
Ratios:
Geometry Problems: Circles
and Triangles:
Rockin' Right Triangle Ratios:
Similarity and Trigonometry
Connections:
Description
Every school child learns that the earth-sun distance is 93 million miles. Yet, determining this distance was a formidable
challenge to the best scientists and mathematicians of the 18th and 19th centuries. The purpose of this lesson is to
use the 2012 Transit of Venus as an opportunity to work through the mathematics to calculate the earth-sun distance.
The only tools needed are basic knowledge of geometry, algebra, and trigonometry. The lesson is self-contained in
that it includes all the data needed to work through the exercise.
Students investigate and discover trigonometric ratios by drawing and measuring side lengths for five triangles that
have equivalent angle measure. Students collect, analyze, and discuss data to draw conclusions. This is the
introductory lesson to facilitate student discovery of trigonometric ratios and allows students to secure a solid
foundation before the use of trigonometry to find missing sides. This lesson has students solving application problems
by finding an unknown angle based on length measurements.
This lesson unit is intended to help you assess how well students are able to use geometric properties to solve
problems. In particular, the lesson will help you identify and help students who have the following difficulties solving
problems by determining the lengths of the sides in right triangles and finding the measurements of shapes by
decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be
different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those
approaches.
Special Right Triangles and the ratios that work when you have to do to learn those ratios for 30-60-90 and 45-45-90
triangles.
The properties of similarity and the corresponding sides of right triangles are used to discover a pattern that leads to
the three trigonometric ratios: sine, cosine, and tangent.
This lesson is using the concept of Inverse Trigonometric Ratios to find the measure of the acute angles in a right
page 1 of 2 THE COPERNICUS' TRAVEL:
triangle and their application in word problems. The Pythagorean Theorem and Special Right Triangles are reviewed
and involved in the problems as well. A summary of the basic applications and a simple method to follow in the
solution of the exercises is shown.
Assessment
Name
Sample 2 - High School
Geometry State Interim
Assessment:
Sample 3 - High School
Geometry State Interim
Assessment:
Description
This is a State Interim Assessment for 9th-12th grade.
This is a State Interim Assessment for 9th-12th grade.
Problem-Solving Task
Name
Description
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern
is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with
pennies give insight into what happens with seven circles in the plane?
Seven Circles I:
Formative Assessment
Name
The Cosine Ratio:
Description
Students are asked to compare the ratio of corresponding sides of two triangles and to explain how this ratio is related
to the cosine of a given angle.
The Sine of 57:
Students are asked to explain what a given sine ratio indicates about a right triangle and if the sine of a specific value
varies depending on the right triangle.
Tutorial
Name
Using Trigonometry to solve
for missing information:
Description
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.
Student Resources
Name
Seven Circles I:
Description
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a
concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give
insight into what happens with seven circles in the plane?
Using Trigonometry to This tutorial will show students how to use trigonometry to solve for missing information in right triangles. This video shows
solve for missing
worked examples using trigonometric ratios to solve for missing information and evaluate other trigonometric ratios.
information:
Parent Resources
Name
Seven Circles I:
Description
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a
concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give
insight into what happens with seven circles in the plane?
page 2 of 2