1 1 30 45 60 45

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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May I please get some help on this . Thank you very much
The image showcases four right-angled triangles with differing angles and side labels. Each triangle has a blank label that needs to be filled in, indicating the missing side lengths.

1. **First Triangle (Leftmost)**
   - **Hypotenuse**: 1
   - **Adjacent Side**: 1/2
   - **Opposite Side**: Not provided (blank label at the bottom of the triangle)
   - **Angles**: Not provided

2. **Second Triangle**
   - **Hypotenuse**: 1
   - **Adjacent Side**: 1/4
   - **Opposite Side**: Not provided (blank label at the bottom of the triangle)
   - **Angles**: Not provided

3. **Third Triangle**
   - **Hypotenuse**: 1
   - **Adjacent Side**: Not provided (blank label)
   - **Opposite Side**: Not provided (blank label)
   - **Angles**: 45°, 45°, 90°

4. **Fourth Triangle (Rightmost)**
   - **Hypotenuse**: 1
   - **Adjacent Side**: Not provided (blank label)
   - **Opposite Side**: Not provided (blank label)
   - **Angles**: 30°, 60°, 90°

**Explanations of Diagrams:**
Each diagram represents a specific type of right-angled triangle with one side labeled and the hypotenuse always being 1. The triangular diagrams are helpful in understanding the relationships between the sides and angles of right triangles, following the principles of trigonometry.

- The first and second triangles appear to lack some side and angle labels, likely to be determined using trigonometric ratios.
- The third triangle is an isosceles right triangle (also known as a 45-45-90 triangle), where both legs should be equal in length.
- The fourth triangle is a 30-60-90 triangle, which has specific known ratios \(1 : \sqrt{3} : 2\) between its sides.

These diagrams are essential for learners to practice identifying and completing the missing parts of the triangles using trigonometric principles.
Transcribed Image Text:The image showcases four right-angled triangles with differing angles and side labels. Each triangle has a blank label that needs to be filled in, indicating the missing side lengths. 1. **First Triangle (Leftmost)** - **Hypotenuse**: 1 - **Adjacent Side**: 1/2 - **Opposite Side**: Not provided (blank label at the bottom of the triangle) - **Angles**: Not provided 2. **Second Triangle** - **Hypotenuse**: 1 - **Adjacent Side**: 1/4 - **Opposite Side**: Not provided (blank label at the bottom of the triangle) - **Angles**: Not provided 3. **Third Triangle** - **Hypotenuse**: 1 - **Adjacent Side**: Not provided (blank label) - **Opposite Side**: Not provided (blank label) - **Angles**: 45°, 45°, 90° 4. **Fourth Triangle (Rightmost)** - **Hypotenuse**: 1 - **Adjacent Side**: Not provided (blank label) - **Opposite Side**: Not provided (blank label) - **Angles**: 30°, 60°, 90° **Explanations of Diagrams:** Each diagram represents a specific type of right-angled triangle with one side labeled and the hypotenuse always being 1. The triangular diagrams are helpful in understanding the relationships between the sides and angles of right triangles, following the principles of trigonometry. - The first and second triangles appear to lack some side and angle labels, likely to be determined using trigonometric ratios. - The third triangle is an isosceles right triangle (also known as a 45-45-90 triangle), where both legs should be equal in length. - The fourth triangle is a 30-60-90 triangle, which has specific known ratios \(1 : \sqrt{3} : 2\) between its sides. These diagrams are essential for learners to practice identifying and completing the missing parts of the triangles using trigonometric principles.
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