Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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## Practice Question: Triangle Side Lengths ### Problem Statement Find the lengths of sides \(a\), \(b\), and \(d\) if \(c = 9\). ### Given Information - \(a = \) [Text box provided for answer] - \(b = \) [Text box provided for answer] - \(d = \dfrac{9}{\sqrt{2}}\) [Correct answer indicated by a checkmark] ### Diagram Explanation Below the problem statement, there is a diagram of a composite geometric figure consisting of a right triangle and a 45°-45°-90° triangle. #### Components of the Diagram: 1. There are two right-angled triangles: - The left triangle has an angle marked as 60°. - The right triangle, adjacent to the left one, is a 45°-45°-90° triangle. 2. Labels are given to the sides of the triangles as follows: - For the larger triangle: - \(a\) is the hypotenuse opposite the 60° angle. - \(b\) is the side adjacent to the 60° angle. - \(c\) is the side opposite the 45° angle (the hypotenuse of the 45°-45°-90° triangle), given as 9 units. - For the smaller 45°-45°-90° triangle: - \(d\), which is perpendicular to \(a\) and adjacent to the 45° angle. - Both legs of this triangle, including \(d\), will be equal, according to the properties of a 45°-45°-90° triangle. ### Solution Summary According to the diagram provided: - The value for \(d\) has been calculated as \(d = \dfrac{9}{\sqrt{2}}\) using the properties of 45°-45°-90° triangles. Use appropriate geometric properties and calculations to find the lengths of sides \(a\) and \(b\).
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Transcribed Image Text:## Practice Question: Triangle Side Lengths ### Problem Statement Find the lengths of sides \(a\), \(b\), and \(d\) if \(c = 9\). ### Given Information - \(a = \) [Text box provided for answer] - \(b = \) [Text box provided for answer] - \(d = \dfrac{9}{\sqrt{2}}\) [Correct answer indicated by a checkmark] ### Diagram Explanation Below the problem statement, there is a diagram of a composite geometric figure consisting of a right triangle and a 45°-45°-90° triangle. #### Components of the Diagram: 1. There are two right-angled triangles: - The left triangle has an angle marked as 60°. - The right triangle, adjacent to the left one, is a 45°-45°-90° triangle. 2. Labels are given to the sides of the triangles as follows: - For the larger triangle: - \(a\) is the hypotenuse opposite the 60° angle. - \(b\) is the side adjacent to the 60° angle. - \(c\) is the side opposite the 45° angle (the hypotenuse of the 45°-45°-90° triangle), given as 9 units. - For the smaller 45°-45°-90° triangle: - \(d\), which is perpendicular to \(a\) and adjacent to the 45° angle. - Both legs of this triangle, including \(d\), will be equal, according to the properties of a 45°-45°-90° triangle. ### Solution Summary According to the diagram provided: - The value for \(d\) has been calculated as \(d = \dfrac{9}{\sqrt{2}}\) using the properties of 45°-45°-90° triangles. Use appropriate geometric properties and calculations to find the lengths of sides \(a\) and \(b\).
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