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5. Which statement is accurate for the right triangle shown below? 50 17 47 sec(8) = 0.34 csc(8) = 1.06 O cot(8) = 2.76 O sec(8) = 0.94

5. Which statement is accurate for the right triangle shown below? 50 17 47 sec(8) = 0.34 csc(8) = 1.06 O cot(8) = 2.76 O sec(8) = 0.94

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 1RP: The origins of the sine function are found in the tables of chords for a circle constructed by the...
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### Question 5: Analyzing Trigonometric Ratios in a Right Triangle **Question:** Which statement is accurate for the right triangle shown below? **Diagram Description:** The diagram depicts a right-angled triangle with one of the angles labeled as \(\theta\) and the opposite side to this angle having a length of 17 units. The hypotenuse of the triangle has a length of 50 units, and the adjacent side to the angle \(\theta\) is 47 units. The other non-right angle in the triangle is labeled as \(\alpha\). **Options:** - \( \circ \) sec(\(\theta\)) = 0.34 - \( \bullet \) csc(\(\theta\)) = 1.06 (this option is marked as selected) - \( \circ \) cot(\(\theta\)) = 2.76 - \( \circ \) sec(\(\theta\)) = 0.94 **Detailed Explanation:** To verify the trigonometric statements, let's break down the trigonometric functions: - **sec(\(\theta\))**: This is the secant function, which equals the hypotenuse divided by the adjacent side. Thus, sec(\(\theta\)) = \( \frac{50}{47} \approx 1.06 \). - **csc(\(\theta\))**: This is the cosecant function, which equals the hypotenuse divided by the opposite side. Thus, csc(\(\theta\)) = \( \frac{50}{17} \approx 2.94 \). - **cot(\(\theta\))**: This is the cotangent function, which equals the adjacent side divided by the opposite side. Thus, cot(\(\theta\)) = \( \frac{47}{17} \approx 2.76 \). From these calculations, we determine the following: - sec(\(\theta\)) should be approximately 1.06, not 0.34 or 0.94. - csc(\(\theta\)) calculated to be approximately 2.94 does not match the selected answer of 1.06. - cot(\(\theta\)) is correctly approximated to 2.76. Thus, cot(\(\theta\)) = 2.76 appears to be the correct statement. If csc(\(\theta\)) =
Transcribed Image Text:### Question 5: Analyzing Trigonometric Ratios in a Right Triangle **Question:** Which statement is accurate for the right triangle shown below? **Diagram Description:** The diagram depicts a right-angled triangle with one of the angles labeled as \(\theta\) and the opposite side to this angle having a length of 17 units. The hypotenuse of the triangle has a length of 50 units, and the adjacent side to the angle \(\theta\) is 47 units. The other non-right angle in the triangle is labeled as \(\alpha\). **Options:** - \( \circ \) sec(\(\theta\)) = 0.34 - \( \bullet \) csc(\(\theta\)) = 1.06 (this option is marked as selected) - \( \circ \) cot(\(\theta\)) = 2.76 - \( \circ \) sec(\(\theta\)) = 0.94 **Detailed Explanation:** To verify the trigonometric statements, let's break down the trigonometric functions: - **sec(\(\theta\))**: This is the secant function, which equals the hypotenuse divided by the adjacent side. Thus, sec(\(\theta\)) = \( \frac{50}{47} \approx 1.06 \). - **csc(\(\theta\))**: This is the cosecant function, which equals the hypotenuse divided by the opposite side. Thus, csc(\(\theta\)) = \( \frac{50}{17} \approx 2.94 \). - **cot(\(\theta\))**: This is the cotangent function, which equals the adjacent side divided by the opposite side. Thus, cot(\(\theta\)) = \( \frac{47}{17} \approx 2.76 \). From these calculations, we determine the following: - sec(\(\theta\)) should be approximately 1.06, not 0.34 or 0.94. - csc(\(\theta\)) calculated to be approximately 2.94 does not match the selected answer of 1.06. - cot(\(\theta\)) is correctly approximated to 2.76. Thus, cot(\(\theta\)) = 2.76 appears to be the correct statement. If csc(\(\theta\)) =
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