Find the lengths of sides a, b, and d if c = 9,
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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![## 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 \(b\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3e9f930-7347-4a0a-9949-50203265dda3%2F7d86e56c-869a-4dba-996e-d00a377bc0e1%2Fn77sow7.jpeg&w=3840&q=75)
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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