Geometry 8-3 Complete Lesson: Trigonometry

By Matt Richardson

Last updated about 3 years ago

26 Questions

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! What is the ratio of the length of the shorter leg to the length of the hypotenuse for △ADF, △AEG, and △ABC? Not all ratios will be used.

5/6
(√5)/6
(√5)/5

△ADF
△AEG
△ABC

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It? Use the figure in the diagram. What is m∠Y to the nearest degree? Enter only a number.

Problem 3 Got It? Reasoning: Suppose you know the lengths of all three sides of a right triangle. Does it matter which trigonometric ratio you use to find the measures of any of the three angles? Explain.

Error Analysis: A student states that sin A > sin X because the lengths of the sides of △ABC are greater than the lengths of △XYZ. What is the student's error? Explain.

Review Lesson 8-2: The length of the hypotenuse of a 30-60-90 triangle is 8. What are the lengths of the legs? Select all that apply.

Review Lessons 3-2 & 6-4: Use rectangle ABCD to match congruent angles.

∠1
∠5
∠3

∠6
∠7
∠11

Vocabulary Review: The Venn diagram shows the relationship between similar and congruent figures. Label each statement as True or False.

True
False

All similar figures are congruent figures.
All congruent figures are similar figures.
Some similar figures are congruent figures.

Vocabulary Review: Which postulate or theorem can you use to verify that the triangles in the diagram are similar.

Use Your Vocabulary: Match each trigonometric ratio with its corresponding side length ratio.

sin B
cos B
tan B

Geometry 8-3 Complete Lesson: Trigonometry

Solve It! What is the ratio of the length of the shorter leg to the length of the hypotenuse for △ADF, △AEG, and △ABC? Not all ratios will be used.

Problem 1 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? Use the figure in the diagram. What is m∠Y to the nearest degree? Enter only a number.

Problem 3 Got It? Reasoning: Suppose you know the lengths of all three sides of a right triangle. Does it matter which trigonometric ratio you use to find the measures of any of the three angles? Explain.

Error Analysis: A student states that sin A > sin X because the lengths of the sides of △ABC are greater than the lengths of △XYZ. What is the student's error? Explain.

Review Lesson 8-2: The length of the hypotenuse of a 30-60-90 triangle is 8. What are the lengths of the legs? Select all that apply.

Review Lessons 3-2 & 6-4: Use rectangle ABCD to match congruent angles.

Vocabulary Review: The Venn diagram shows the relationship between similar and congruent figures. Label each statement as True or False.

Vocabulary Review: Which postulate or theorem can you use to verify that the triangles in the diagram are similar.

Use Your Vocabulary: Identify the ratio of the length of the longer leg to the length of the shorter leg.

Use Your Vocabulary: Match each trigonometric ratio with its corresponding side length ratio.

Reasoning: Suppose △ABC is a right isosceles triangle. What would the tangent of ∠B equal? Enter only a number.

Reflection: Math Success