Use Inverse Trigonometric Ratios to solve these triangles. ### Triangle ProblemsBelow are four right-angled triangles, each labeled with side lengths and an angle θ. Use trigonometric concepts to solve for the unknowns in each scenario.#### Diagram Descriptions:1. **Triangle 5** - **Vertices:** A, B, C - **Side Lengths:** - AC = 7.7 - BC = 14 - **Angle:** θ is located at vertex A - **Right Angle:** Located at vertex C2. **Triangle 6** - **Vertices:** A, B, C - **Side Lengths:** - AB = 5 - BC = 4 - **Angle:** θ is located at vertex B - **Right Angle:** Located at vertex C3. **Triangle 7** - **Vertices:** A, B, C - **Side Lengths:** - AB = 11 - BC = 4.4 - **Angle:** θ is located at vertex A - **Right Angle:** Located at vertex C4. **Triangle 8** - **Vertices:** A, B, C - **Side Lengths:** - BC = 3 - AC = 3 - **Angle:** θ is located at vertex B - **Right Angle:** Located at vertex C### Instructions:- Use appropriate trigonometric functions (sine, cosine, tangent) to find missing angles or side lengths.- Ensure to verify results using the Pythagorean theorem where applicable.- Consider each triangle independently and solve using known side lengths and angles.These triangles can be used as practice problems to better understand the application of trigonometry in solving right triangles.

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Answered: 5) 7) 7.7 A A C 11 14 Ө C B 4.4 6) 8) B…

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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Use Inverse Trigonometric Ratios to solve these triangles.

### Triangle Problems

Below are four right-angled triangles, each labeled with side lengths and an angle θ. Use trigonometric concepts to solve for the unknowns in each scenario.

#### Diagram Descriptions:

1. **Triangle 5**
- **Vertices:** A, B, C
- **Side Lengths:**
- AC = 7.7
- BC = 14
- **Angle:** θ is located at vertex A
- **Right Angle:** Located at vertex C

2. **Triangle 6**
- **Vertices:** A, B, C
- **Side Lengths:**
- AB = 5
- BC = 4
- **Angle:** θ is located at vertex B
- **Right Angle:** Located at vertex C

3. **Triangle 7**
- **Vertices:** A, B, C
- **Side Lengths:**
- AB = 11
- BC = 4.4
- **Angle:** θ is located at vertex A
- **Right Angle:** Located at vertex C

4. **Triangle 8**
- **Vertices:** A, B, C
- **Side Lengths:**
- BC = 3
- AC = 3
- **Angle:** θ is located at vertex B
- **Right Angle:** Located at vertex C

### Instructions:

- Use appropriate trigonometric functions (sine, cosine, tangent) to find missing angles or side lengths.
- Ensure to verify results using the Pythagorean theorem where applicable.
- Consider each triangle independently and solve using known side lengths and angles.

These triangles can be used as practice problems to better understand the application of trigonometry in solving right triangles.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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