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

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

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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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**.
Transcribed Image Text:### 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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