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tan IS For problems 23 – 25, find the following sides and angles of the right triangle. (Round answers to 2 significant digits) A = 28°,c = 1.8 1 80 180 - 28 2 152 23. B = 180 28 a 90+28 :118 24. a = 17 25. b = 28 C b. A

tan IS For problems 23 – 25, find the following sides and angles of the right triangle. (Round answers to 2 significant digits) A = 28°,c = 1.8 1 80 180 - 28 2 152 23. B = 180 28 a 90+28 :118 24. a = 17 25. b = 28 C b. A

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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last question a b

## Problem 22: **Question:** The angle of elevation of a lighthouse from a boat is 15°. If the top of the lighthouse is 225 ft above sea level, how far away is the boat from the base of the lighthouse? (Round the answer to 3 significant digits) ### Given: - Angle of elevation: 15° - Height of the lighthouse: 225 ft ### Solution: 1. Using trigonometry: tan(θ) = opposite/adjacent 2. Here, tan(15°) = 225 / AB 3. AB = 225 / tan(15°) 4. Calculation yields AB ≈ 839.7 ft 5. Rounded to 3 significant digits, AB = 840 ft ### Answer: The boat is approximately 840 ft away from the base of the lighthouse. ## Problems 23-25: **Question:** Find the following sides and angles of the right triangle. (Round answers to 2 significant digits) ### Diagram Description: A right triangle with: - Angle A = 28° - Side c = 1.8 - Side BC is denoted as a = 7 ### Solution Process: #### Problem 23: - To find angle B: - Angle B = 90° - A - B = 90° - 28° = 62° #### Problem 24: - To find side a: - Use trigonometry: a = c * tan(A) - Calculate a = 7 #### Problem 25: - To find side b: - Use the Pythagorean theorem or other trigonometric identities as appropriate ### Answers: 23. \( B = 62° \) 24. \( a = 7 \) 25. \( b = \text{To be calculated} \)
Transcribed Image Text:## Problem 22: **Question:** The angle of elevation of a lighthouse from a boat is 15°. If the top of the lighthouse is 225 ft above sea level, how far away is the boat from the base of the lighthouse? (Round the answer to 3 significant digits) ### Given: - Angle of elevation: 15° - Height of the lighthouse: 225 ft ### Solution: 1. Using trigonometry: tan(θ) = opposite/adjacent 2. Here, tan(15°) = 225 / AB 3. AB = 225 / tan(15°) 4. Calculation yields AB ≈ 839.7 ft 5. Rounded to 3 significant digits, AB = 840 ft ### Answer: The boat is approximately 840 ft away from the base of the lighthouse. ## Problems 23-25: **Question:** Find the following sides and angles of the right triangle. (Round answers to 2 significant digits) ### Diagram Description: A right triangle with: - Angle A = 28° - Side c = 1.8 - Side BC is denoted as a = 7 ### Solution Process: #### Problem 23: - To find angle B: - Angle B = 90° - A - B = 90° - 28° = 62° #### Problem 24: - To find side a: - Use trigonometry: a = c * tan(A) - Calculate a = 7 #### Problem 25: - To find side b: - Use the Pythagorean theorem or other trigonometric identities as appropriate ### Answers: 23. \( B = 62° \) 24. \( a = 7 \) 25. \( b = \text{To be calculated} \)
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