Download MAFS.912.G-SRT.4 - Apply trigonometry to general triangles

Standard 4 : Apply trigonometry to general triangles
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Number: MAFS.912.G-SRT.4
Title: Apply trigonometry to general triangles
Type: Cluster
Subject: Mathematics
Grade: 912
Domain: Geometry: Similarity, Right Triangles, &
Trigonometry
Related Standards
Code
MAFS.912.G-SRT.4.9
MAFS.912.G-SRT.4.10
MAFS.912.G-SRT.4.11
Description
Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular
to the opposite side.
Prove the Laws of Sines and Cosines and use them to solve problems.
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right
triangles (e.g., surveying problems, resultant forces).
Related Resources
Perspectives Video: Professional/Enthusiast
Name
Celestial Navigation and
Trigonometry:
Description
Lost at sea? We can use a sextant, the stars, and trigonometry to find our location!
Lesson Plan
Name
Description
Deriving and Applying the Law Students will be introduced to a derivation of the Law of Sines and apply the Law of Sines to solve triangles.
of Sines:
This lesson introduces the law of sine. It is designed to give students practice in using the law to guide understanding.
Following the Law of Sine:
The summative assessment requires students to use the law of sine to plan a city project.
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
Geometry Problems: Circles
problems by determining the lengths of the sides in right triangles and finding the measurements of shapes by
and Triangles:
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.
In this lesson, students determine when to use the Law of Cosine and/or the Law of Sine to calculate the measures
The Laws of Sine and Cosine: of sides and angles of non-right triangles.
Will You Survive?:
Students are stranded on a desert island and will need to use the law of sines in order to find the quickest path to a
rescue vessel.
Note: This is not an introductory lesson for the standard.
Educational Game
Name
Law of Cosines Game 2:
Law of Sines Game:
Description
Play a game using the law of cosines to find the measure of angles in non-right triangles or the cosine of an angle.
Answer questions with and without a calculator. Select Teach Me to learn how to set up equations with trig ratios and
solve for the measure of angles prior to beginning play. Hints and feedback are available as you play.
Play a game using the law of sines to solve for the length of sides in non-right triangles or use trig ratios to set up an
equation. Answer questions with and without a calculator. Students may select Teach Me to learn how to set up
equations with trig ratios and solve for the length of sides prior to beginning play. Hints and feedback are provided to
page 1 of 3 players.
Law of Sines Game 2:
Play a game using the law of sines to find the measure of angles in non-right triangles or the sine of an angle. Answer
questions with and without a calculator. Students may select Teach Me to learn how to set up equations with trig
ratios and solve for the measure of angles prior to beginning play. Hints and feedback are provided to players.
Video/Audio/Animation
Name
MIT BLOSSOMS - The Juice
Seller’s Problem:
Description
"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")
Virtual Manipulative
Name
Right Triangle Calculator:
Triangle Solver:
Description
"Free online calculator will calculate the side lengths and angles for any right triangle. Just input any valid combination of
sides and/or angles, and let the calculator do the rest! This free tool also draws a downloadable image of your triangle."
(from Math Worksheets Go!)
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.
Problem-Solving Task
Name
Seven Circles III:
Description
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.
Tutorial
Name
The basics of trigonometry:
Description
This tutorial shows the basics of trigonometry, sine, cosine, and tangent. Students will determine oppopsite sides,
adjacent sides and the hypotenuse of right triangles.
Student Resources
Title
Law of Cosines Game 2:
Description
Play a game using the law of cosines to find the measure of angles in non-right triangles or the cosine of an angle.
Answer questions with and without a calculator. Select Teach Me to learn how to set up equations with trig ratios and
solve for the measure of angles prior to beginning play. Hints and feedback are available as you play.
Law of Sines Game:
Play a game using the law of sines to solve for the length of sides in non-right triangles or use trig ratios to set up an
equation. Answer questions with and without a calculator. Students may select Teach Me to learn how to set up
equations with trig ratios and solve for the length of sides prior to beginning play. Hints and feedback are provided to
players.
Law of Sines Game 2:
Play a game using the law of sines to find the measure of angles in non-right triangles or the sine of an angle. Answer
questions with and without a calculator. Students may select Teach Me to learn how to set up equations with trig
ratios and solve for the measure of angles prior to beginning play. Hints and feedback are provided to players.
Seven Circles III:
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.
The basics of trigonometry:
Triangle Solver:
This tutorial shows the basics of trigonometry, sine, cosine, and tangent. Students will determine oppopsite sides,
adjacent sides and the hypotenuse of right triangles.
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.
page 2 of 3 Parent Resources
Title
Seven Circles III:
Triangle Solver:
Description
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.
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.
page 3 of 3