### Solving for the Missing Side in a Right TriangleIn 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.**#### DiagramThere 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!

Answered: Image /qna-images/answer/e42df973-9b6f-4773-a4c9-31804eb509b0.jpg

Answered: Solve for the missing side in the right…

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

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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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

### 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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