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Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. Find sin 0.

Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. Find sin 0.

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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**Educational Content: Trigonometric Functions and the Pythagorean Theorem** Below are questions related to finding the lengths of the missing sides in right-angled triangles using the Pythagorean Theorem and then determining specific trigonometric functions. --- **QUESTION 38** **Problem Statement:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Question:** Find sin θ. **Diagram:** - Right triangle ABC with: - AB (opposite side to θ) = 4 - AC (adjacent side to θ) = 7 **Answer Choices:** - \(\frac{4 \sqrt{65}}{65}\) - \(\frac{4 \sqrt{65}}{65}\) - \(\frac{7 \sqrt{65}}{65}\) - \(\frac{\sqrt{65}}{7}\) **Selected Answer:** \(\frac{4 \sqrt{65}}{65}\) --- **QUESTION 39** **Problem Statement:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Question:** Find sin θ. **Diagram:** - Right triangle ABC with: - AB (opposite side to θ) = 3 - AC (adjacent side to θ) = 2 **Answer Choices:** - \(\frac{\sqrt{13}}{2}\) - \(\frac{\sqrt{13}}{13}\) - \(\frac{2 \sqrt{13}}{13}\) - \(\frac{\sqrt{13}}{3}\) **Selected Answer:** \(\frac{2 \sqrt{13}}{13}\) --- **QUESTION 40** **Problem Statement:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Question:** Find csc θ. **Diagram:** - Right triangle ABC with: - AB (opposite side to θ) = 2 - AC (adjacent side to θ) = 3
Transcribed Image Text:**Educational Content: Trigonometric Functions and the Pythagorean Theorem** Below are questions related to finding the lengths of the missing sides in right-angled triangles using the Pythagorean Theorem and then determining specific trigonometric functions. --- **QUESTION 38** **Problem Statement:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Question:** Find sin θ. **Diagram:** - Right triangle ABC with: - AB (opposite side to θ) = 4 - AC (adjacent side to θ) = 7 **Answer Choices:** - \(\frac{4 \sqrt{65}}{65}\) - \(\frac{4 \sqrt{65}}{65}\) - \(\frac{7 \sqrt{65}}{65}\) - \(\frac{\sqrt{65}}{7}\) **Selected Answer:** \(\frac{4 \sqrt{65}}{65}\) --- **QUESTION 39** **Problem Statement:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Question:** Find sin θ. **Diagram:** - Right triangle ABC with: - AB (opposite side to θ) = 3 - AC (adjacent side to θ) = 2 **Answer Choices:** - \(\frac{\sqrt{13}}{2}\) - \(\frac{\sqrt{13}}{13}\) - \(\frac{2 \sqrt{13}}{13}\) - \(\frac{\sqrt{13}}{3}\) **Selected Answer:** \(\frac{2 \sqrt{13}}{13}\) --- **QUESTION 40** **Problem Statement:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Question:** Find csc θ. **Diagram:** - Right triangle ABC with: - AB (opposite side to θ) = 2 - AC (adjacent side to θ) = 3
### Educational Website Transcription --- #### QUESTION 44 **Prompt:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Graph:** A right triangle labeled as follows: - Hypotenuse: \( \overline{AB} \) - Vertical leg: \( \overline{BC} = 5 \) - Horizontal leg: \( \overline{AC} = 6 \) **Question:** Find \(\sec \theta\). **Answer Choices:** - \( \sec \theta \) - ( ) \(\frac{6}{5}\) - ( ) \(\frac{\sqrt{61}}{5}\) - ( ) \(\frac{5\sqrt{61}}{61}\) - ( ) \(\frac{\sqrt{61}}{6}\) - (•) \( \frac{6.5}{61} \) --- #### QUESTION 45 **Prompt:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Graph:** A right triangle labeled as follows: - Hypotenuse: \( \overline{AB} \) - Vertical leg: \( \overline{BC} = 3 \) - Horizontal leg: \( \overline{AC} = 2 \) **Question:** Find \(\sec \theta\). **Answer Choices:** - \( \sec \theta \) - ( ) \( \frac{2}{\sqrt{13}} \) - (•) \( \frac{\sqrt{13}}{2} \) - ( ) \( \frac{3\sqrt{13}}{2} \) - ( ) \( \frac{\sqrt{13}}{3} \) - ( ) \( \frac{\sqrt{13}}{2} \) --- #### QUESTION 46 **Prompt:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Graph:** A right triangle labeled as follows: - Hypotenuse
Transcribed Image Text:### Educational Website Transcription --- #### QUESTION 44 **Prompt:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Graph:** A right triangle labeled as follows: - Hypotenuse: \( \overline{AB} \) - Vertical leg: \( \overline{BC} = 5 \) - Horizontal leg: \( \overline{AC} = 6 \) **Question:** Find \(\sec \theta\). **Answer Choices:** - \( \sec \theta \) - ( ) \(\frac{6}{5}\) - ( ) \(\frac{\sqrt{61}}{5}\) - ( ) \(\frac{5\sqrt{61}}{61}\) - ( ) \(\frac{\sqrt{61}}{6}\) - (•) \( \frac{6.5}{61} \) --- #### QUESTION 45 **Prompt:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Graph:** A right triangle labeled as follows: - Hypotenuse: \( \overline{AB} \) - Vertical leg: \( \overline{BC} = 3 \) - Horizontal leg: \( \overline{AC} = 2 \) **Question:** Find \(\sec \theta\). **Answer Choices:** - \( \sec \theta \) - ( ) \( \frac{2}{\sqrt{13}} \) - (•) \( \frac{\sqrt{13}}{2} \) - ( ) \( \frac{3\sqrt{13}}{2} \) - ( ) \( \frac{\sqrt{13}}{3} \) - ( ) \( \frac{\sqrt{13}}{2} \) --- #### QUESTION 46 **Prompt:** Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. **Graph:** A right triangle labeled as follows: - Hypotenuse
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