# Standard 1: Define and use trigonometric ratios, identities or functions to solve problems. Export Print
General Information
Number: MA.912.T.1
Title: Define and use trigonometric ratios, identities or functions to solve problems.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Trigonometry

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.912.T.1.AP.1
Select a trigonometric ratio for acute angles in right triangles limited to sine or cosine.
MA.912.T.1.AP.2
Given a mathematical and/or real-world problem involving right triangles, solve using trigonometric ratio or the Pythagorean Theorem.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

## Formative Assessments

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.

Type: Formative Assessment

The Cosine Ratio:

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.

Type: Formative Assessment

Sine and Cosine:

Students are asked to explain the relationship between sine and cosine of the acute angles of a right triangle.

Type: Formative Assessment

Right Triangle Relationships:

Students are given the sine and cosine of angle measures and asked to identify the sine and cosine of their complements.

Type: Formative Assessment

Finding Sine:

Students are asked to explain the relationship between sine and cosine of complementary angles.

Type: Formative Assessment

Patterns in the 30-60-90 Table:

Students are asked to use 30-60-90 triangle relationships to observe and explain the relationship between sin 30 and cos 60 (or sin 60 and cos 30).

Type: Formative Assessment

Pyramid Height:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

Washington Monument:

Students are asked to find the angle of elevation in a real world situation modeled by a right triangle.

Type: Formative Assessment

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.

Type: Formative Assessment

River Width:

Students are asked to find an unknown length in a real world context requiring right triangle trigonometry.

Type: Formative Assessment

Perilous Plunge:

Students are asked to find an unknown length in a real world context requiring right triangle trigonometry.

Type: Formative Assessment

Lighthouse Keeper:

Students are asked to find the difference between two lengths in a real world context requiring right triangle trigonometry.

Type: Formative Assessment

Holiday Lights:

Students are asked to solve a problem in a real world context requiring the use of the Pythagorean Theorem.

Type: Formative Assessment

Will It Fit?:

Students are asked to solve a problem in a real world context using the Pythagorean Theorem.

Type: Formative Assessment

TV Size:

Students are asked to solve a problem in a real world context requiring the use of the Pythagorean Theorem.

Type: Formative Assessment

## Lesson Plans

Discovering Trigonometric Ratios:

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.

Type: Lesson Plan

Just Plane Ol' Area!:

Students will construct various figures on coordinate planes and calculate the perimeter and area. Use of the Pythagorean theorem will be required.

Type: Lesson Plan

Are You Pulling My Trig?:

This lesson is an introduction of the application of trigonometric ratios. Students will solve real-world word problems using trigonometric ratios of sine, cosine and tangent.

Type: Lesson Plan

Let's Get "Triggy":

This lesson helps students discover trigonometric ratios and how to apply them to find the measure of sides and angles of a right triangle.  Students will think about problems, discuss concepts with a partner and then share ideas with the class. Students will collaborate and offer supportive coaching to help deepen each other’s understanding.

Type: Lesson Plan

## Original Student Tutorial

Around the World with Right Triangles:

Learn how to use trigonometric ratios to find the heights of famous monuments and solve a real-world application in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Oceanography & Math:

A discussion describing ocean currents studied by a physical oceanographer and how math is involved.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Lost at sea? We can use a sextant, the stars, and trigonometry to find our location!

Type: Perspectives Video: Professional/Enthusiast

## Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

## Original Student Tutorial

Around the World with Right Triangles:

Learn how to use trigonometric ratios to find the heights of famous monuments and solve a real-world application in this interactive tutorial.

Type: Original Student Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.