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ABCD is a kite, so AC I DB and DE = EB. Calculate the length of AC, to t nearest tenth of a centimeter. 8 cm E В 14 cm 10 cm A

ABCD is a kite, so AC I DB and DE = EB. Calculate the length of AC, to t nearest tenth of a centimeter. 8 cm E В 14 cm 10 cm A

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 38E
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**Understanding Kites in Geometry** In this exercise, we are given a kite \(ABCD\) with the following properties and measurements: - \( AC \perp DB \), meaning the diagonals \(AC\) and \(DB\) are perpendicular to each other. - \( DE = EB \), indicating that the diagonal \(DB\) is bisected into two equal parts by point \(E\). The given dimensions are: - \( DE = EB = 14 \, \text{cm} \) - \( AD = 10 \, \text{cm} \) - \( CD = 8 \, \text{cm} \) **Objective:** Calculate the length of the diagonal \( AC \), to the nearest tenth of a centimeter. **Visual Description:** The provided diagram of kite \(ABCD\) shows: - Point \(C\) at the top. - Point \(A\) at the bottom. - Point \(D\) on the left side. - Point \(B\) on the right side. - The intersection point \(E\) of the diagonals \(AC\) and \(DB\) with \(DE = EB = 14 \, \text{cm}\), indicating that \(DB = 2 \times 14 \, \text{cm} = 28 \, \text{cm}\). From the properties of kites and the given dimensions, we can use the Pythagorean theorem within the smaller right triangles formed by splitting the kite across its diagonals. **Step-by-Step Calculation:** 1. **Identify the Right Triangles:** - Triangle \(ADE\) with sides \(AD = 10 \, \text{cm}\), \(DE = 14 \, \text{cm}\), and \(AE = \text{unknown}\). - Triangle \(CDE\) with sides \(CD = 8 \, \text{cm}\), \(DE = 14 \, \text{cm}\), and \(CE = \text{unknown}\). 2. **Calculate \(AE\) (using \( \triangle ADE\) ): \(AD^2 = AE^2 + DE^2\) \(10^2 = AE^2 + 14^2\) \(100 = AE^2 + 196\) \(AE^2 = 100 - 196 = -96\
Transcribed Image Text:**Understanding Kites in Geometry** In this exercise, we are given a kite \(ABCD\) with the following properties and measurements: - \( AC \perp DB \), meaning the diagonals \(AC\) and \(DB\) are perpendicular to each other. - \( DE = EB \), indicating that the diagonal \(DB\) is bisected into two equal parts by point \(E\). The given dimensions are: - \( DE = EB = 14 \, \text{cm} \) - \( AD = 10 \, \text{cm} \) - \( CD = 8 \, \text{cm} \) **Objective:** Calculate the length of the diagonal \( AC \), to the nearest tenth of a centimeter. **Visual Description:** The provided diagram of kite \(ABCD\) shows: - Point \(C\) at the top. - Point \(A\) at the bottom. - Point \(D\) on the left side. - Point \(B\) on the right side. - The intersection point \(E\) of the diagonals \(AC\) and \(DB\) with \(DE = EB = 14 \, \text{cm}\), indicating that \(DB = 2 \times 14 \, \text{cm} = 28 \, \text{cm}\). From the properties of kites and the given dimensions, we can use the Pythagorean theorem within the smaller right triangles formed by splitting the kite across its diagonals. **Step-by-Step Calculation:** 1. **Identify the Right Triangles:** - Triangle \(ADE\) with sides \(AD = 10 \, \text{cm}\), \(DE = 14 \, \text{cm}\), and \(AE = \text{unknown}\). - Triangle \(CDE\) with sides \(CD = 8 \, \text{cm}\), \(DE = 14 \, \text{cm}\), and \(CE = \text{unknown}\). 2. **Calculate \(AE\) (using \( \triangle ADE\) ): \(AD^2 = AE^2 + DE^2\) \(10^2 = AE^2 + 14^2\) \(100 = AE^2 + 196\) \(AE^2 = 100 - 196 = -96\
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