Which equation can Jada use to find the value of x? ### Understanding Tangent in Right TrianglesThe image shows a right triangle with the sides labeled as follows:- **Vertical side (pole)**: 3 units- **Horizontal side**: 4 units- **Hypotenuse (rope)**: Unlabeled but can be deduced using the Pythagorean theorem.The angle adjacent to the vertical side and opposite the horizontal side is denoted as $ x^\circ $.In a right triangle, the tangent of an angle $ x $ is defined as the ratio of the opposite side to the adjacent side. Hence, for the given triangle, the tangent would be:\[ \tan(x) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{3}{4} \]The question posed is to select the correct representation of the tangent function for the angle $ x $.### Multiple-Choice QuestionThere are four options provided for identifying the correct trigonometric relationship:- **Option A**: $ \tan(x) = \frac{3}{4} $ - **Option B**: $ x = \tan\left( \frac{3}{4} \right) $- **Option C**: $ x = \tan\left( \frac{4}{3} \right) $- **Option D**: $ \tan(x) = \frac{4}{3} $From the earlier calculation:\[ \tan(x) = \frac{3}{4} \]Hence, the correct answer is **Option A**.

Answered: pole rope to A tan(x) = 3. tan 4 3/4 3.

Math

Geometry

pole rope to A tan(x) = 3. tan 4 3/4 3.

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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Equations and inequalities describe the relationship between two mathematical expressions.

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Question

Which equation can Jada use to find the value of x?

### Understanding Tangent in Right Triangles

The image shows a right triangle with the sides labeled as follows:

- **Vertical side (pole)**: 3 units
- **Horizontal side**: 4 units
- **Hypotenuse (rope)**: Unlabeled but can be deduced using the Pythagorean theorem.

The angle adjacent to the vertical side and opposite the horizontal side is denoted as $ x^\circ $.

In a right triangle, the tangent of an angle $ x $ is defined as the ratio of the opposite side to the adjacent side. Hence, for the given triangle, the tangent would be:

\[ \tan(x) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{3}{4} \]

The question posed is to select the correct representation of the tangent function for the angle $ x $.

### Multiple-Choice Question

There are four options provided for identifying the correct trigonometric relationship:

- **Option A**: $ \tan(x) = \frac{3}{4} $
- **Option B**: $ x = \tan\left( \frac{3}{4} \right) $
- **Option C**: $ x = \tan\left( \frac{4}{3} \right) $
- **Option D**: $ \tan(x) = \frac{4}{3} $

From the earlier calculation:
\[ \tan(x) = \frac{3}{4} \]

Hence, the correct answer is **Option A**.

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