Download CCGPS Analytic Geometry Unit 2 Right Angle Trigonometry Parent

CCGPS Analytic Geometry
Unit 2
Right Angle Trigonometry
Student Learning Targets: I can…
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Use the characteristics of similar figures to justify the trigonometric
ratios.
Define trigonometric ratios for acute angles in a right triangle as
tan<A, sin<A, and cos<A.
2
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2
Use division and the Pythagorean Theorem (a + b = c ) to prove that
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2
sin A + cos A = 1.
Define complementary angles.
Calculate sine and cosine ratios for acute angles in a right triangle
when given two side lengths.
Solve right triangles by finding the measure of all sides and angles in
the triangles.
Solve application problems involving right triangles, including angle of
elevation and depression, navigation, and surveying.
Key Vocabulary
Acute angle: an angle whose measure is between 0 and 90 degrees.
Angle-angle similarity: If two angles of one triangle are congruent to two
corresponding angles in another triangle, then the triangles are similar.
Complementary angle: are two angles whose sum is 90 degrees.
Constant: a quantity that does not change its value.
Cosine: the ratio of the length of the side adjacent to an acute angle to
the length of the hypotenuse.
Cosine ratio: is the ratio of the length of the adjacent side to that of the
hypotenuse.
Right triangle: a triangle with exactly one right angle.
Sine: is the ratio of the length of the opposite side to that of the
hypotenuse
Sine ratio: is the ratio of the length of the opposite side to that of the
hypotenuse.
Tangent: ratio of the length of the side opposite an acute angle in a right
triangle to the side adjacent to the angle. The tangent of an angle is equal
to the sine of the angle divided by the cosine of the angle.
Trigonometry: deals with the relationships between the sides and the
angles of triangles and the calculations based on them.
Parent Guide
What your student should know & do at home
Important Understandings and Concepts
What should my student already know before I begin…..
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Able to measure angles with a protractor.
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Understand how to label angles and sides in triangles.
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Able to convert fractions into decimals.
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Able to divide with decimals.
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Able to solve for one unknown number in a ratio or proportion.
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Understand the properties of similar triangles.
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Understand and apply the properties of dilations.
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Understand how to set up and use ratios.
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Convert measurement units within the same system (example: from inches to feet).
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Able to manipulate the Pythagorean Theorem given any two sides of a right triangle.
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Able to set up and solve problems using the Pythagorean Theorem.
Learning at a Glance
. Students should remember that similar triangles are triangles with corresponding congruent angles
and corresponding sides that are in proportion.
CCGPS Analytic Geometry
Unit 2
Right Angle Trigonometry
Sample Problems
Parent Guide
What your student should know & do at home
How Can You Help Your Student?
Interactive Learning Lessons
Learn Zillion – Find right triangle angle measures using inverse sine function
Learn Zillion - Find right triangle angle measures using inverse cosine function
Learn Zillion - Find right triangle angle measures using inverse tangent function
Learn Zillion - Apply trigonometry and the Pythagorean Theorem in context
Interactive Learning Games
http://www.regentsprep.org/Regents/math/algtrig/ATT1/PracSpecial.htm
http://www.regentsprep.org/Regents/math/algtrig/ATT6/PracCofunc.htm
Playing games is a wonderful way to practice skills at home in a fun environment. Stack-n-Pack
books contain several math games covering math concepts from Kindergarten through High
School. Stack-n-Pack card games may be checked out from your school (contact your school’s
Parent Liaison) or purchased online: Stack-n-Pack Mathematics Card Games for K-HS .
Stack-n-Pack Geometry
• Right Triangle Geometry game
Sample Problem 2
Find the second acute angle of a right triangle given that the first acute angle
has measure of 39°.
Solution: 51 degrees
Sample Problem 3
Complete the following statement: If sin 30° = ½, then the cos ____ = ½.
Solution: 60 degrees
Sample Problem 4
Find: sin A, sin B, cos A, cos B
2
2
2
Solution: 5 + 12 = c ; c = 169; c = 13
sin A =5/13 , sin B =12/13 , cos A = 12/13 , cos B = 5/13