Right A EFG has its right angle at F, EG = 8, and FG = 6. What is the value of the trigonometric ratio of an angle of the triangle? Drag a value to each box to match the trigonometric ratio with its value. cot G sin E sec G 4√7 3√7 7 7 حظر انت 53 1 5/0 2 334 3 4 5 6 7 8 9 10 Next

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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## Trigonometric Ratios in Right-Angle Triangles

Consider a right triangle \( \triangle EFG \) with a right angle at \( F \). In this triangle:
- \( EG = 8 \)
- \( FG = 6 \)

### Problem Statement

Determine the values of the following trigonometric ratios for the given triangle:
1. \( \cot G \)
2. \( \sin E \)
3. \( \sec G \)

Drag a value to each box to match the trigonometric ratio with its correct value from the provided options.

### Available Values to Choose From:

\[ \frac{4}{3} \quad \frac{\sqrt{7}}{3} \quad \frac{4\sqrt{7}}{7} \quad \frac{3\sqrt{7}}{7} \quad \frac{\sqrt{7}}{8} \quad \frac{3}{4} \]

### Answer Boxes:

- **cot \( G \)**
- **sin \( E \)**
- **sec \( G \)**

### Steps to Solve:

1. **Finding \( \cot G \)**:
   - Use the definition of cotangent in a right triangle: \( \cot G = \frac{\text{adjacent}}{\text{opposite}} \).

2. **Finding \( \sin E \)**:
   - Use the definition of sine in a right triangle: \( \sin E = \frac{\text{opposite}}{\text{hypotenuse}} \).

3. **Finding \( \sec G \)**:
   - Use the definition of secant in a right triangle: \( \sec G = \frac{\text{hypotenuse}}{\text{adjacent}} \).

### Diagram Analysis

The problem must have a visual representation of the triangle, and the student should be able to apply the trigonometric definitions to determine the correct values from the given options.

---

*Note: This problem is a part of a sequence, labeled as "1 2 3 4 5 6 7 8 9 10" with the current step being "1". The "Next" button at the bottom right suggests that this is part of a multi-step educational exercise.*
Transcribed Image Text:## Trigonometric Ratios in Right-Angle Triangles Consider a right triangle \( \triangle EFG \) with a right angle at \( F \). In this triangle: - \( EG = 8 \) - \( FG = 6 \) ### Problem Statement Determine the values of the following trigonometric ratios for the given triangle: 1. \( \cot G \) 2. \( \sin E \) 3. \( \sec G \) Drag a value to each box to match the trigonometric ratio with its correct value from the provided options. ### Available Values to Choose From: \[ \frac{4}{3} \quad \frac{\sqrt{7}}{3} \quad \frac{4\sqrt{7}}{7} \quad \frac{3\sqrt{7}}{7} \quad \frac{\sqrt{7}}{8} \quad \frac{3}{4} \] ### Answer Boxes: - **cot \( G \)** - **sin \( E \)** - **sec \( G \)** ### Steps to Solve: 1. **Finding \( \cot G \)**: - Use the definition of cotangent in a right triangle: \( \cot G = \frac{\text{adjacent}}{\text{opposite}} \). 2. **Finding \( \sin E \)**: - Use the definition of sine in a right triangle: \( \sin E = \frac{\text{opposite}}{\text{hypotenuse}} \). 3. **Finding \( \sec G \)**: - Use the definition of secant in a right triangle: \( \sec G = \frac{\text{hypotenuse}}{\text{adjacent}} \). ### Diagram Analysis The problem must have a visual representation of the triangle, and the student should be able to apply the trigonometric definitions to determine the correct values from the given options. --- *Note: This problem is a part of a sequence, labeled as "1 2 3 4 5 6 7 8 9 10" with the current step being "1". The "Next" button at the bottom right suggests that this is part of a multi-step educational exercise.*
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