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In this square, find the value of each variable. f 6p- 3 Зр +4 e = degrees degrees degrees h D I3D

In this square, find the value of each variable. f 6p- 3 Зр +4 e = degrees degrees degrees h D I3D

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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### Problem Statement: **In this square, find the value of each variable.** ### Diagram Description: The diagram shows a square with a diagonal line dividing it into two right triangles. The variables are assigned as follows: - **e** is the angle adjacent to the variables **g** and **h**. - **f** is the angle adjacent to the variables **h** and the expression **3p + 4**. - **g** is the angle adjacent to the variables **e** and **h**. - **h** is the length of the side adjacent to the variables **e** and **f**. - One side of the square is labeled as **3p + 4**. - The diagonal of the square is labeled as **6p - 3**. ### Given Tasks: Calculate the values of the following variables: - \( e = \) ______ degrees - \( f = \) ______ degrees - \( g = \) ______ degrees - \( h = \) ______ - \( p = \) ______ ### Explanatory Steps: 1. **Identify the properties of a square:** - All four angles are 90 degrees. - All sides are equal in length. - The diagonals of a square are equal in length and bisect each other at 90 degrees angles. 2. **Analyze the given expressions and relationships:** - The sides are expressed in terms of \( p \). - The diagonal's length can be calculated using the Pythagorean theorem in right triangles formed by dividing the square. 3. **Solve for each variable step-by-step:** - Use the properties of the square and the Pythagorean theorem to find the side length \( h \). - Substitute the side length into the expressions to solve for \( p \). - Use trigonometric relationships or properties of angles in the square to determine angles \( e \), \( f \), and \( g \).
Transcribed Image Text:### Problem Statement: **In this square, find the value of each variable.** ### Diagram Description: The diagram shows a square with a diagonal line dividing it into two right triangles. The variables are assigned as follows: - **e** is the angle adjacent to the variables **g** and **h**. - **f** is the angle adjacent to the variables **h** and the expression **3p + 4**. - **g** is the angle adjacent to the variables **e** and **h**. - **h** is the length of the side adjacent to the variables **e** and **f**. - One side of the square is labeled as **3p + 4**. - The diagonal of the square is labeled as **6p - 3**. ### Given Tasks: Calculate the values of the following variables: - \( e = \) ______ degrees - \( f = \) ______ degrees - \( g = \) ______ degrees - \( h = \) ______ - \( p = \) ______ ### Explanatory Steps: 1. **Identify the properties of a square:** - All four angles are 90 degrees. - All sides are equal in length. - The diagonals of a square are equal in length and bisect each other at 90 degrees angles. 2. **Analyze the given expressions and relationships:** - The sides are expressed in terms of \( p \). - The diagonal's length can be calculated using the Pythagorean theorem in right triangles formed by dividing the square. 3. **Solve for each variable step-by-step:** - Use the properties of the square and the Pythagorean theorem to find the side length \( h \). - Substitute the side length into the expressions to solve for \( p \). - Use trigonometric relationships or properties of angles in the square to determine angles \( e \), \( f \), and \( g \).
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