The image features a trigonometry problem involving a right triangle and multiple-choice answers to identify which trigonometric equation can be used to find the measure of angle BAC.### Description of the Right Triangle Diagram:- **Vertices**: The triangle has vertices labeled A, B, and C.- **Sides**: - The side opposite to angle BAC is labeled 5 units. - The side adjacent to angle BAC is labeled 12 units. - The hypotenuse (the side opposite the right angle at vertex C) is labeled 13 units. ### Diagram Explanation:- **Point A** is at the top vertex of the triangle.- **Point B** is at the bottom-right vertex.- **Point C** is at the bottom-left vertex and indicates the right angle with a small red square.- **Line Segment AC** is the side opposite angle BAC and is 5 units long.- **Line Segment CB** is the side adjacent to angle BAC and is 12 units long.- **Line Segment AB** is the hypotenuse of the right triangle and is 13 units long.### Question:"Which equation can be used to find the measure of angle BAC?"### Answer Choices:1. $\tan^{-1} \left(\frac{5}{12}\right) = x$2. $\tan^{-1} \left(\frac{12}{5}\right) = x$3. $\cos^{-1} \left(\frac{12}{13}\right) = x$4. $\cos^{-1} \left(\frac{13}{12}\right) = x$### Detailed Explanation:To determine the correct equation for finding the measure of angle BAC, we need to consider the trigonometric ratios associated with a right triangle:- **Tangent (tan)**: \[ \tan(\text{{angle}}) = \frac{\text{{opposite}}}{\text{{adjacent}}} \] For angle BAC, the opposite side is 5 units and the adjacent side is 12 units. Thus, the correct tangent-based equation is: \[ \tan^{-1} \left(\frac{5}{12}\right) = x \]- **Cosine (cos)**: \[ \cos(\text{{angle}}) = \frac{\text{{adj

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Description: The image features a trigonometry problem involving a right triangle and multiple-choice answers to identify which trigonometric equation can be used to find the measure of angle BAC.### Description of the Right Triangle Diagram:- **Vertices**: The

In this question we will use basic of geometry i.e use of trigonometric ratios. We will simply apply…

Answered: B O tan-1 cos 13 13 O cos 12

Math

Geometry

B O tan-1 cos 13 13 O cos 12

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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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

The image features a trigonometry problem involving a right triangle and multiple-choice answers to identify which trigonometric equation can be used to find the measure of angle BAC.

### Description of the Right Triangle Diagram:
- **Vertices**: The triangle has vertices labeled A, B, and C.
- **Sides**:
- The side opposite to angle BAC is labeled 5 units.
- The side adjacent to angle BAC is labeled 12 units.
- The hypotenuse (the side opposite the right angle at vertex C) is labeled 13 units.

### Diagram Explanation:
- **Point A** is at the top vertex of the triangle.
- **Point B** is at the bottom-right vertex.
- **Point C** is at the bottom-left vertex and indicates the right angle with a small red square.
- **Line Segment AC** is the side opposite angle BAC and is 5 units long.
- **Line Segment CB** is the side adjacent to angle BAC and is 12 units long.
- **Line Segment AB** is the hypotenuse of the right triangle and is 13 units long.

### Question:
"Which equation can be used to find the measure of angle BAC?"

### Answer Choices:
1. $\tan^{-1} \left(\frac{5}{12}\right) = x$
2. $\tan^{-1} \left(\frac{12}{5}\right) = x$
3. $\cos^{-1} \left(\frac{12}{13}\right) = x$
4. $\cos^{-1} \left(\frac{13}{12}\right) = x$

### Detailed Explanation:
To determine the correct equation for finding the measure of angle BAC, we need to consider the trigonometric ratios associated with a right triangle:

- **Tangent (tan)**:
\[
\tan(\text{{angle}}) = \frac{\text{{opposite}}}{\text{{adjacent}}}
\]
For angle BAC, the opposite side is 5 units and the adjacent side is 12 units. Thus, the correct tangent-based equation is:
\[
\tan^{-1} \left(\frac{5}{12}\right) = x
\]

- **Cosine (cos)**:
\[
\cos(\text{{angle}}) = \frac{\text{{adj

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