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Find the exact value of x in the figure. O A. 8/6 16/3 OB. 3 600 16/6 Oc. 3 O D. 83 450 16

Find the exact value of x in the figure. O A. 8/6 16/3 OB. 3 600 16/6 Oc. 3 O D. 83 450 16

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Geometry Problem: Determining the Exact Value of x #### Problem Statement: Find the exact value of \(x\) in the given figure. #### Diagram Explanation: - We have a right triangle with one angle marked as 45° and another angle marked as 60°. - One side adjacent to the 45° angle is labeled as "16". #### Answer Choices: A. \(\frac{8 \sqrt{6}}{3}\) B. \(\frac{16 \sqrt{3}}{3}\) C. \(\frac{16 \sqrt{6}}{3}\) D. \(8 \sqrt{3}\) ### How to Solve: 1. **Identify angles and relationships:** The triangle in question is a right triangle, and we know that with a 45° angle, it is also closely related to 45°-45°-90° and 30°-60°-90° triangles. 2. **Use special right triangle properties:** - In a 45°-45°-90° triangle, the lengths of the legs are equal, and the hypotenuse is the leg length multiplied by \(\sqrt{2}\). - In a 30°-60°-90° triangle, the sides are in the ratio 1 : \(\sqrt{3}\) : 2. 3. **Calculate based on side length information provided:** Utilize the properties of 30°-60°-90° triangle formulae or trigonometric identities to determine the unknown side \(x\). ### Solutions Explained: If we consider the given side (adjacent to the 45° and opposite to the 60°) and apply trigonometric properties (like sine, cosine relating the lengths of sides and the angles provided), we solve for \(x\). After solving, we select from the answer choices: A. \(\frac{8 \sqrt{6}}{3}\) B. \(\frac{16 \sqrt{3}}{3}\) C. \(\frac{16 \sqrt{6}}{3}\) D. \(8 \sqrt{3}\) Keep in mind, the side ratios and the methodologies applied within such geometric constraints essentially guide to a derived choice showing correct mathematical approach. ### Note: The exact method to reach the solution involves breaking and solving step-by-step angular approaches and confirming through selection which meets the
Transcribed Image Text:### Geometry Problem: Determining the Exact Value of x #### Problem Statement: Find the exact value of \(x\) in the given figure. #### Diagram Explanation: - We have a right triangle with one angle marked as 45° and another angle marked as 60°. - One side adjacent to the 45° angle is labeled as "16". #### Answer Choices: A. \(\frac{8 \sqrt{6}}{3}\) B. \(\frac{16 \sqrt{3}}{3}\) C. \(\frac{16 \sqrt{6}}{3}\) D. \(8 \sqrt{3}\) ### How to Solve: 1. **Identify angles and relationships:** The triangle in question is a right triangle, and we know that with a 45° angle, it is also closely related to 45°-45°-90° and 30°-60°-90° triangles. 2. **Use special right triangle properties:** - In a 45°-45°-90° triangle, the lengths of the legs are equal, and the hypotenuse is the leg length multiplied by \(\sqrt{2}\). - In a 30°-60°-90° triangle, the sides are in the ratio 1 : \(\sqrt{3}\) : 2. 3. **Calculate based on side length information provided:** Utilize the properties of 30°-60°-90° triangle formulae or trigonometric identities to determine the unknown side \(x\). ### Solutions Explained: If we consider the given side (adjacent to the 45° and opposite to the 60°) and apply trigonometric properties (like sine, cosine relating the lengths of sides and the angles provided), we solve for \(x\). After solving, we select from the answer choices: A. \(\frac{8 \sqrt{6}}{3}\) B. \(\frac{16 \sqrt{3}}{3}\) C. \(\frac{16 \sqrt{6}}{3}\) D. \(8 \sqrt{3}\) Keep in mind, the side ratios and the methodologies applied within such geometric constraints essentially guide to a derived choice showing correct mathematical approach. ### Note: The exact method to reach the solution involves breaking and solving step-by-step angular approaches and confirming through selection which meets the
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