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Standard 4 : Apply trigonometry to general
triangles
This document was generated on CPALMS - www.cpalms.org
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
Description
Celestial Navigation and Trigonometry:
Lost at sea? We can use a sextant, the stars, and
trigonometry to find our location!
Lesson Plan
Name
Description
Students will be introduced to a derivation of the
Deriving and Applying the Law of Sines: Law of Sines and apply the Law of Sines to solve
triangles.
This lesson introduces the law of sine. It is
designed to give students practice in using the law
Following the Law of Sine:
to guide understanding. 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 problems by
determining the lengths of the sides in right
Geometry Problems: Circles and Triangles: 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.
In this lesson, students determine when to use the
Law of Cosine and/or the Law of Sine to calculate
The Laws of Sine and Cosine:
the measures of sides and angles of non-right
triangles.
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.
Will You Survive?:
Note: This is not an introductory lesson for the
standard.
Educational Game
Name
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
Law of Sines Game:
Law of Sines Game 2:
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 players.
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
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
MIT BLOSSOMS - The Juice Seller’s Problem: 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
Description
Law of Cosines Game 2:
Law of Sines Game:
Law of Sines Game 2:
Seven Circles III:
The basics of trigonometry:
Triangle Solver:
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 players.
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.
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.
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.
Parent Resources
Title
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.
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.