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.

**Number:**MAFS.912.G-SRT.3

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

**Type:**Cluster

**Subject:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Similarity, Right Triangles, & Trigonometry

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Lesson Study Resource Kit

## Original Student Tutorial

## Perspectives Video: Expert

## Presentation/Slideshow

## Problem-Solving Tasks

## Teaching Idea

## Tutorials

## Video/Audio/Animation

## Virtual Manipulatives

## Student Resources

## Original Student Tutorial

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.

Type: Original Student Tutorial

## Presentation/Slideshow

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers.

Type: Presentation/Slideshow

## Problem-Solving Tasks

Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin.

Type: Problem-Solving Task

This problem solving task asks students to find the area of an equilateral triangle.

Type: Problem-Solving Task

This task engages students in an open-ended modeling task that uses similarity of right triangles.

Type: Problem-Solving Task

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle which is crucial for many further developments in the subject.

Type: Problem-Solving Task

This provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function.

Type: Problem-Solving Task

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?

Type: Problem-Solving Task

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found.

Type: Problem-Solving Task

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Type: Problem-Solving Task

## Tutorials

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.

Type: Tutorial

This tutorial gives an introduction to trigonometry. This resource discusses the three basic trigonometry functions, sine, cosine, and tangent.

Type: Tutorial

This video discusses how to figure out the horizontal displacement for a projectile launched at an angle.

Type: Tutorial

## Virtual Manipulatives

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin.

Type: Problem-Solving Task

This problem solving task asks students to find the area of an equilateral triangle.

Type: Problem-Solving Task

This task engages students in an open-ended modeling task that uses similarity of right triangles.

Type: Problem-Solving Task

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle which is crucial for many further developments in the subject.

Type: Problem-Solving Task

This provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function.

Type: Problem-Solving Task

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?

Type: Problem-Solving Task

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found.

Type: Problem-Solving Task

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Type: Problem-Solving Task

## Virtual Manipulatives

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative