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7.) Maria goes to a school that is rectangular in shape. There is a walkway from the entrance that goes to her math class. The floor plan is shown below. What would be the equation to find the distance between her class and the cafeteria? Select all that apply. 1400 Math Class Restroopr D Entrance Library Cafeteria 32 tan x = tan 32 = 1400 1400 Option 1 Option 2 cos 32 1400 (tan 32) = x 1400 Option 3 Option 4 tan 32 X = 1400 Option 5

7.) Maria goes to a school that is rectangular in shape. There is a walkway from the entrance that goes to her math class. The floor plan is shown below. What would be the equation to find the distance between her class and the cafeteria? Select all that apply. 1400 Math Class Restroopr D Entrance Library Cafeteria 32 tan x = tan 32 = 1400 1400 Option 1 Option 2 cos 32 1400 (tan 32) = x 1400 Option 3 Option 4 tan 32 X = 1400 Option 5

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
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Maria goes to a school that is rectangular in shape. There is a walkway from the entrance that goes to her math class. The floor plan is shown below. What would be the equation to find the distance between her class and the cafeteria? Select all that apply.
**Problem 7 Analysis - Walkway Distance Calculation in a Rectangular School Building** Consider the floor plan of Maria's school which is depicted as a rectangle. Maria needs to find the distance between her math class and the cafeteria. The diagram below helps in visualizing the problem: **Diagram Details:** - Shape: Rectangle ABCD - Points: A (Entrance), B, C (Math Class), D (Cafeteria) - Line AC: Walkway from the Entrance to Math Class with distance "Restroom" across it - Known dimensions: - AB = 32 units - BC (opposite distance) = 1400 units - Distance from Math Class to Cafeteria is unknown (denoted as 'X') **Mathematical Equations Provided:** - **Option 1:** \(\tan x = \frac{32}{1400}\) - **Option 2:** \(\tan 32 = \frac{x}{1400}\) - **Option 3:** \(\cos 32 = \frac{x}{1400}\) - **Option 4:** \(1400 (\tan 32) = x\) - **Option 5:** \(X = \frac{\tan 32}{1400}\) **Evaluation:** - The floor plan structure is critical for determining which trigonometric identity will effectively assess the distance (X) from the math class to the cafeteria. - Recognize that we need to resolve the distance as a function of identified components, using the tan function correctly since it relates the opposite side to the adjacent side in a rectangular geometric setting. **Providing Correct Options:** Given the slope and layout in the calcuations, we use the tangent relation: 1. \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}} \Longrightarrow \tan 32^\circ = \frac{x}{1400}\) 2. Simplifying to get the correct measures. Therefore, from the provided options: - **Correct Equation(s):** - **Option 2:** \(\tan 32 = \frac{x}{1400}\) - **Option 4:** \(1400 (\tan 32) = x\) These options provide viable ways to calculate the distance between the math class (point C) and the cafeteria (point D) based on the given trigonometric relationships in
Transcribed Image Text:**Problem 7 Analysis - Walkway Distance Calculation in a Rectangular School Building** Consider the floor plan of Maria's school which is depicted as a rectangle. Maria needs to find the distance between her math class and the cafeteria. The diagram below helps in visualizing the problem: **Diagram Details:** - Shape: Rectangle ABCD - Points: A (Entrance), B, C (Math Class), D (Cafeteria) - Line AC: Walkway from the Entrance to Math Class with distance "Restroom" across it - Known dimensions: - AB = 32 units - BC (opposite distance) = 1400 units - Distance from Math Class to Cafeteria is unknown (denoted as 'X') **Mathematical Equations Provided:** - **Option 1:** \(\tan x = \frac{32}{1400}\) - **Option 2:** \(\tan 32 = \frac{x}{1400}\) - **Option 3:** \(\cos 32 = \frac{x}{1400}\) - **Option 4:** \(1400 (\tan 32) = x\) - **Option 5:** \(X = \frac{\tan 32}{1400}\) **Evaluation:** - The floor plan structure is critical for determining which trigonometric identity will effectively assess the distance (X) from the math class to the cafeteria. - Recognize that we need to resolve the distance as a function of identified components, using the tan function correctly since it relates the opposite side to the adjacent side in a rectangular geometric setting. **Providing Correct Options:** Given the slope and layout in the calcuations, we use the tangent relation: 1. \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}} \Longrightarrow \tan 32^\circ = \frac{x}{1400}\) 2. Simplifying to get the correct measures. Therefore, from the provided options: - **Correct Equation(s):** - **Option 2:** \(\tan 32 = \frac{x}{1400}\) - **Option 4:** \(1400 (\tan 32) = x\) These options provide viable ways to calculate the distance between the math class (point C) and the cafeteria (point D) based on the given trigonometric relationships in
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