Geometry
DB Unit 5 Trigonometry
Name:
Date:
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Learning Targets for Unit 5 (Modules 13 & 14)
Big Idea: Similarity, Right Triangles, and Trigonometry. Define trig ratios and solve problems
involving right triangles.
Trigonometry Standards and Practice Problems
(Additional practice problems: Odd problems at the end of each section)
Mastery
(-, , +)
Review Simplifying Radicals, Angle Relationships, & Special Right Triangles
Find the complementary angle.
Find the supplementary angle
1a. 20°
1b. 67°
2a. 80°
2b. 34°
Find the remaining angle(s) for ABC.
3a. 𝑚∠𝐴 = 50°, 𝑚∠𝐵 = 40°
3b. 𝑚∠𝐵 = 70° and ∠𝐴 ≅ ∠𝐶
3c. ABC is similar to DEF and 𝑚∠𝐷 = 70°, 𝑚∠𝐹 = 50°
Find the value of x. Give the answer in simplest radical form.
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2/2016
Geometry
Trigonometry Standards and Practice Problems
(Additional practice problems: Odd problems at the end of each section)
Similarity in Right Triangles and Sine, Cosine, and Tangent Ratios
G.SRT.6, MP.4 Modeling Understand that by similarity, the side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of trig ratios for acute angles.
13.1 Tangent Ratio
13.2 Sine and Cosine Ratio
8-2 Find the sine, cosine, and tangent of an acute angle
Use trig ratios to find side lengths in right triangles and to solve real-world problems
8-3 Use trig ratios to find angle measures in right triangles and to solve rea-world problems
1. Find the sine and cosine, and tangent of angle A.
Given a right triangle △XYZ where ∠Z is a right angle, XY = 53, YZ = 28, and XZ = 45, find
the following rounded to the nearest hundredth.
2. sinX
3. cosX
4. tanX
5. A painter is placing a ladder to reach the third story window, which is 20 feet above
the ground and makes an angle with the ground of 70°. How far out from the building
does the base of the ladder need to be positioned?
√3
6. Given the value of 𝑐𝑜𝑠30° = , write the sine of a complementary angle. Use an
2
expression relating trigonometric ratios of complementary angles.
Use a special right triangle to write each trigonometric ratio as a fraction.
7. tan 60°
8. cos 60°
9. sin 60°
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.
10. sin 12°
11. cos 59°
12. tan 17°
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Geometry
Mastery
(-, , +)
Trigonometry Standards and Practice Problems
(Additional practice problems: Odd problems at the end of each section)
13.
Reginald is planning to fence his back yard.
Every side of the yard except for the side along
the house is to be fenced, and fencing costs
$3.50/yd. How much will the fencing cost?
Find each length. Round to the nearest hundredth.
Solving Right Triangles
G.SRT.8, MP.2 Reasoning Use trigonometric ratios and the Pythagorean Theorem to solve
right triangles in applied problems.
13.3 Special Right Triangles
13.4 Problem Solving with Trig
8-2 Find the sine, cosine, and tangent of an acute angle
17. Given an isosceles right triangle DEF with m∠F = 90° and DE = 7, find the length of
the other two sides.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Geometry
Mastery
(-, , +)
Trigonometry Standards and Practice Problems
(Additional practice problems: Odd problems at the end of each section)
18. Find the lengths of the other two sides of the following triangle. Find exact answers in
order of least to greatest. A 30°-60°-90° triangle with a hypotenuse of length 14.
19. Find the area of the following triangle, rounded to the nearest tenth. A triangle △ABC,
where m∠C = 127°, AC = 5, and BC = 9.
20. What is the area of a regular hexagon with a distance from its center to a vertex of 1
cm? (Hint: A regular hexagon can be divided into six equilateral triangles.)
Solving Right Triangles
G-SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
14.1 Law of Sines
14.2 Law of Cosines
8-5 Use Law of Sines and Law of Cosines
21. Find the area of the triangle. Round to the nearest tenth.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Geometry
Mastery
(-, , +)
Trigonometry Standards and Practice Problems
(Additional practice problems: Odd problems at the end of each section)
22. Solve the triangle. Round to the nearest tenth.
Find the area of the triangle. Round to the nearest tenth.
23.
24.
Solve each triangle. Round to the nearest tenth.
25.
26.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Geometry
Mastery
(-, , +)
Trigonometry Standards and Practice Problems
(Additional practice problems: Odd problems at the end of each section)
Solve each triangle. Round to the nearest tenth.
27.
Mastery
(-, , +)
28.
Answer these questions to summarize the important concepts.
1) Explain the trigonometric ratios.
2) Explain what solving a right triangle means.
3) Explain why the sine and cosine of an acute angle are always between 0 and 1.
4) How would you go about finding the area of a regular pentagon given the distance from its
center to the vertices?
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Geometry