Geometry 10-5 Complete Lesson: Trigonometry and Area

By Matt Richardson

Last updated about 3 years ago

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! The pennant shown is in the shape of an isosceles triangle. The measure of the vertex angle is 20 degrees. What is the area of the pennant? Hint: Consider using right triangle trigonometry. Round to the nearest square inch and enter your response in this format: 981 square inches

Solve It! Explain how you found your answer to the previous item.

Problem 1 Got It?

Problem 2 Got It? A tabletop has the shape of a regular decagon with a radius of 9.5 in. What is the area of the tabletop to the nearest square inch? Enter your response in this format: 981 square inches

Problem 2 Got It? Reasoning: Suppose the radius of a regular polygon is doubled. How does the area of the polygon change? Explain.

Problem 3 Got It?

Error Analysis: Your classmate needs to find the area of a regular pentagon with 8-cm sides. To find the apothem, he sets up and solves a trigonometric ratio. What error did he make? Explain.

Review Lesson 10-4: What is the scale factor of the smaller octagon to the larger octagon?

Review Lesson 10-4: The area of the larger octagon is 391.1 in². What is the area of the smaller octagon to the nearest square inch? Enter your response in this format: 39 square inches

Review Lesson 8-5: Use the Law of Sines to find the value of x. Round to the nearest hundredth. Enter your response in this format: 21.30 m

Review Lesson 8-5: Use the Law of Sines to find the value of y. Round to the nearest hundredth. Enter your response in this format: 21.30 m

Review Lesson 1-8: Sort the items in ascending order (least on top) based on the value of the number that fills in each blank.

A circle with radius 7 has diameter __?__.
A circle with diameter 15 has radius __?__.
A circle with radius 6 has diameter __?__.

Vocabulary Review: Fill in the blank to complete the sentence.

Area is the number of ? units needed to cover a given surface.

Vocabulary Review: What is the formula for the area of a triangle?

Use Your Vocabulary: Write only the word trigonometry or trigonometric to complete the sentence. The sine, cosine, and tangent ratios are ? ratios.

Use Your Vocabulary: Write only the word trigonometry or trigonometric to complete the sentence. This year I am studying ? in math.

Use Your Vocabulary: Match each ratio of side lengths from a right triangle with the trigonometric ratio it represents.

cosine
sine
tangent

Geometry 10-5 Complete Lesson: Trigonometry and Area

Solve It! The pennant shown is in the shape of an isosceles triangle. The measure of the vertex angle is 20 degrees. What is the area of the pennant? Hint: Consider using right triangle trigonometry. Round to the nearest square inch and enter your response in this format: 981 square inches

Solve It! Explain how you found your answer to the previous item.

Problem 1 Got It?

Problem 2 Got It? A tabletop has the shape of a regular decagon with a radius of 9.5 in. What is the area of the tabletop to the nearest square inch? Enter your response in this format: 981 square inches

Problem 2 Got It? Reasoning: Suppose the radius of a regular polygon is doubled. How does the area of the polygon change? Explain.

Problem 3 Got It?

Error Analysis: Your classmate needs to find the area of a regular pentagon with 8-cm sides. To find the apothem, he sets up and solves a trigonometric ratio. What error did he make? Explain.

Review Lesson 10-4: What is the scale factor of the smaller octagon to the larger octagon?

Review Lesson 10-4: The area of the larger octagon is 391.1 in². What is the area of the smaller octagon to the nearest square inch? Enter your response in this format: 39 square inches

Review Lesson 8-5: Use the Law of Sines to find the value of x. Round to the nearest hundredth. Enter your response in this format: 21.30 m

Review Lesson 8-5: Use the Law of Sines to find the value of y. Round to the nearest hundredth. Enter your response in this format: 21.30 m

Review Lesson 1-8: Sort the items in ascending order (least on top) based on the value of the number that fills in each blank.

Vocabulary Review: Fill in the blank to complete the sentence. Area is the number of __?__ units needed to cover a given surface.

Vocabulary Review: What is the formula for the area of a triangle?

Use Your Vocabulary: Write only the word trigonometry or trigonometric to complete the sentence. The sine, cosine, and tangent ratios are __?__ ratios.

Use Your Vocabulary: Write only the word trigonometry or trigonometric to complete the sentence. This year I am studying __?__ in math.

Use Your Vocabulary: Match each ratio of side lengths from a right triangle with the trigonometric ratio it represents.

Reflection: Math Success

Vocabulary Review: Fill in the blank to complete the sentence.

Area is the number of ? units needed to cover a given surface.

Use Your Vocabulary: Write only the word trigonometry or trigonometric to complete the sentence. The sine, cosine, and tangent ratios are ? ratios.

Use Your Vocabulary: Write only the word trigonometry or trigonometric to complete the sentence. This year I am studying ? in math.