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Consider ARST, as shown. If cos R = which of the following answer choices are possible trigonometric ratios? Select all that apply R 15 T S,

Consider ARST, as shown. If cos R = which of the following answer choices are possible trigonometric ratios? Select all that apply R 15 T S,

Elementary Geometry For College Students, 7e
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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Consider △RST△RST, as shown.  If  cosR=35cos⁡R=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.
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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