Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A. sin A = cos A = tan A = A (Type an integer or a simplified fraction.) (Type an integer or a simplified fraction.) (Type an integer or a simplified fraction.) 37 35 12 C
Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A. sin A = cos A = tan A = A (Type an integer or a simplified fraction.) (Type an integer or a simplified fraction.) (Type an integer or a simplified fraction.) 37 35 12 C
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Trigonometric Ratios of a Right Triangle
#### Diagram Description
The given diagram is a right triangle labelled \( \triangle ABC \) with \( \angle C \) as the right angle. The side lengths of the triangle are as follows:
- Side \( AB \) (hypotenuse) = 37 units
- Side \( BC \) (opposite to angle \( A \)) = 12 units
- Side \( AC \) (adjacent to angle \( A \)) = 35 units
#### Explanation
To find the trigonometric ratios for \( \sin A \), \( \cos A \), and \( \tan A \), we use the following definitions for a right triangle:
- **Sine (sin)** of an angle: \( \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \)
- **Cosine (cos)** of an angle: \( \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)
- **Tangent (tan)** of an angle: \( \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \)
#### Formulas
Given \( \triangle ABC \):
- For \( \sin A \):
\[
\sin A = \frac{BC}{AB} = \frac{12}{37}
\]
- For \( \cos A \):
\[
\cos A = \frac{AC}{AB} = \frac{35}{37}
\]
- For \( \tan A \):
\[
\tan A = \frac{BC}{AC} = \frac{12}{35}
\]
#### Input Fields
To practice and ensure understanding, students are encouraged to type their answers in the provided fields below:
- \( \sin A = \) [Input Field] (Type an integer or a simplified fraction.)
- \( \cos A = \) [Input Field] (Type an integer or a simplified fraction.)
- \( \tan A = \) [Input Field] (Type an integer or a simplified fraction.)
Feel free to use these calculations to check your understanding of basic trigonometric ratios in right triangles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F959a643c-45ff-4cba-bf81-f285af0e5e62%2Fd44180b3-457c-4ac3-b36f-ac8a614a8965%2F58h9vnv_processed.png&w=3840&q=75)
Transcribed Image Text:### Trigonometric Ratios of a Right Triangle
#### Diagram Description
The given diagram is a right triangle labelled \( \triangle ABC \) with \( \angle C \) as the right angle. The side lengths of the triangle are as follows:
- Side \( AB \) (hypotenuse) = 37 units
- Side \( BC \) (opposite to angle \( A \)) = 12 units
- Side \( AC \) (adjacent to angle \( A \)) = 35 units
#### Explanation
To find the trigonometric ratios for \( \sin A \), \( \cos A \), and \( \tan A \), we use the following definitions for a right triangle:
- **Sine (sin)** of an angle: \( \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \)
- **Cosine (cos)** of an angle: \( \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)
- **Tangent (tan)** of an angle: \( \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \)
#### Formulas
Given \( \triangle ABC \):
- For \( \sin A \):
\[
\sin A = \frac{BC}{AB} = \frac{12}{37}
\]
- For \( \cos A \):
\[
\cos A = \frac{AC}{AB} = \frac{35}{37}
\]
- For \( \tan A \):
\[
\tan A = \frac{BC}{AC} = \frac{12}{35}
\]
#### Input Fields
To practice and ensure understanding, students are encouraged to type their answers in the provided fields below:
- \( \sin A = \) [Input Field] (Type an integer or a simplified fraction.)
- \( \cos A = \) [Input Field] (Type an integer or a simplified fraction.)
- \( \tan A = \) [Input Field] (Type an integer or a simplified fraction.)
Feel free to use these calculations to check your understanding of basic trigonometric ratios in right triangles.
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