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Solve for the missing side in the right triangle below. Leave answers in simplified radical form or round to the nearest hundredth. Rectangular Snip 30° D 3 in F Side length d =

Solve for the missing side in the right triangle below. Leave answers in simplified radical form or round to the nearest hundredth. Rectangular Snip 30° D 3 in F Side length d =

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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### Solving for the Missing Side in a Right Triangle In the problem below, you are given a right triangle DEF. You are tasked with solving for the missing side \( d \). Please leave your answers in simplified radical form or rounded to the nearest hundredth. #### Problem Statement **Solve for the missing side in the right triangle below. Leave answers in simplified radical form or round to the nearest hundredth.** #### Diagram There is a right triangle DEF with: - Angle D = 30° - DE = \( f \) (hypotenuse) - DF = 3 inches (adjacent side) - EF = \( d \) (opposite side to angle D) ```plaintext E | |\ | \ d | \ f | \ | \ | \ D |______F 3 in ``` #### Question **Side length \( d \) = _______** #### Multiple-Choice Answers - \( \sqrt{3} \) - \( 2\sqrt{3} \) - \( \frac{20}{\sqrt{7}} \) - \( \frac{2}{\sqrt{6}} \) Choose the correct option based on your calculation. --- ### Steps to Solve: 1. Identify the relationship between the given sides and the angle. 2. Apply trigonometric identities as needed (e.g., sine, cosine, or tangent). 3. Simplify your answer based on the given choice forms or round as necessary. Good luck!
Transcribed Image Text:### Solving for the Missing Side in a Right Triangle In the problem below, you are given a right triangle DEF. You are tasked with solving for the missing side \( d \). Please leave your answers in simplified radical form or rounded to the nearest hundredth. #### Problem Statement **Solve for the missing side in the right triangle below. Leave answers in simplified radical form or round to the nearest hundredth.** #### Diagram There is a right triangle DEF with: - Angle D = 30° - DE = \( f \) (hypotenuse) - DF = 3 inches (adjacent side) - EF = \( d \) (opposite side to angle D) ```plaintext E | |\ | \ d | \ f | \ | \ | \ D |______F 3 in ``` #### Question **Side length \( d \) = _______** #### Multiple-Choice Answers - \( \sqrt{3} \) - \( 2\sqrt{3} \) - \( \frac{20}{\sqrt{7}} \) - \( \frac{2}{\sqrt{6}} \) Choose the correct option based on your calculation. --- ### Steps to Solve: 1. Identify the relationship between the given sides and the angle. 2. Apply trigonometric identities as needed (e.g., sine, cosine, or tangent). 3. Simplify your answer based on the given choice forms or round as necessary. Good luck!
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