Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
Consider △RST△RST, as shown. If cosR=35cosR=35 which of the following answer choices are possible trigonometric ratios? Select all that apply.
![### Trigonometric Ratios in Right Triangle RST
**Triangle Diagram:**
Consider the right triangle \( \triangle RST \), where \(\angle S\) is the right angle, \( RS = 15 \) units, and \( cos(R) = \frac{3}{5} \). The triangle is displayed with \( R \) at the top vertex, \( S \) at the bottom right vertex (right angle), and \( T \) at the bottom left vertex.
**Question:**
Which of the following answer choices are possible trigonometric ratios? Select all that apply.
**Answer Choices:**
- [ ] \( \sin R = \frac{4}{5} \)
- [ ] \( \sin T = \frac{4}{5} \)
- [ ] \( \cos T = \frac{12}{15} \)
- [ ] \( \sin T = \frac{12}{15} \)
- [ ] \( \cos R = \frac{12}{15} \)
**Explanation of the Diagram:**
- The triangle diagram is a right triangle with labelled sides and angles.
- The hypotenuse is \( RT \).
- Given that \( \cos R = \frac{3}{5} \), this implies that the adjacent side to \( \angle R \) (which is \( RS \)) is 3 units when the hypotenuse \( RT \) is scaled to 5 units.
- The side opposite \( \angle R \) (which is \( TS \)) needs to be calculated using the Pythagorean theorem, or understanding typical trigonometric ratios in a 3-4-5 triangle. Given that \( RS = 15 \), scaling the triangle by \(5\) gives \( TS = 4(3) = 12 \).
Ensure to verify the options by considering the trigonometric definitions with known side lengths.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56c0d7e7-dec0-442e-807e-93dee8ab6b46%2F5ff6bdd8-1417-4078-938e-1b9bd0c19360%2F1jz8sjj_processed.png&w=3840&q=75)
Transcribed Image Text:### Trigonometric Ratios in Right Triangle RST
**Triangle Diagram:**
Consider the right triangle \( \triangle RST \), where \(\angle S\) is the right angle, \( RS = 15 \) units, and \( cos(R) = \frac{3}{5} \). The triangle is displayed with \( R \) at the top vertex, \( S \) at the bottom right vertex (right angle), and \( T \) at the bottom left vertex.
**Question:**
Which of the following answer choices are possible trigonometric ratios? Select all that apply.
**Answer Choices:**
- [ ] \( \sin R = \frac{4}{5} \)
- [ ] \( \sin T = \frac{4}{5} \)
- [ ] \( \cos T = \frac{12}{15} \)
- [ ] \( \sin T = \frac{12}{15} \)
- [ ] \( \cos R = \frac{12}{15} \)
**Explanation of the Diagram:**
- The triangle diagram is a right triangle with labelled sides and angles.
- The hypotenuse is \( RT \).
- Given that \( \cos R = \frac{3}{5} \), this implies that the adjacent side to \( \angle R \) (which is \( RS \)) is 3 units when the hypotenuse \( RT \) is scaled to 5 units.
- The side opposite \( \angle R \) (which is \( TS \)) needs to be calculated using the Pythagorean theorem, or understanding typical trigonometric ratios in a 3-4-5 triangle. Given that \( RS = 15 \), scaling the triangle by \(5\) gives \( TS = 4(3) = 12 \).
Ensure to verify the options by considering the trigonometric definitions with known side lengths.
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