The triangles are similar. Find the missing side, angle or value of the variable. b CH a = 56° b = 6 cm O 6 cm O 90° O 34° O 56°

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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### Educational Content Transcription

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**Question 3**

**Problem Statement:**

The triangles are similar. Find the missing side, angle, or value of the variable.

**Given:**

- Two triangles: Triangle XYZ and Triangle QPR
  - Angle X = a = 56°
  - Side QR = b = 6 cm

**Diagram Explanation:**

- Triangle XYZ is on the left, oriented with angle X known to be 56°.
  - YQ is visually indicated to be parallel to PR, making the triangles similar by angle similarity.

- Triangle QPR is on the right with side QR labeled as 6 cm, and angle QPR similar to angle XYZ.

**Multiple Choice Options:**

- O 6 cm
- O 90°
- O 34°
- O 56°

---

**Diagram Details:**

- The diagram includes two similar triangles, labeled XYZ and QPR. 
  - XYZ has angles with the following measurements:
    - X = 56°
    - Y and Z are not specified but are marked to imply similarity to QPR.
  - QPR includes:
    - Angle at Q measuring the same as angle X from triangle XYZ which is 56°
    - Side QR measures 6 cm. 

---

- This content is designed for educational purposes to assist in understanding the relationships in similar triangles and the properties of angles and sides.
Transcribed Image Text:### Educational Content Transcription --- **Question 3** **Problem Statement:** The triangles are similar. Find the missing side, angle, or value of the variable. **Given:** - Two triangles: Triangle XYZ and Triangle QPR - Angle X = a = 56° - Side QR = b = 6 cm **Diagram Explanation:** - Triangle XYZ is on the left, oriented with angle X known to be 56°. - YQ is visually indicated to be parallel to PR, making the triangles similar by angle similarity. - Triangle QPR is on the right with side QR labeled as 6 cm, and angle QPR similar to angle XYZ. **Multiple Choice Options:** - O 6 cm - O 90° - O 34° - O 56° --- **Diagram Details:** - The diagram includes two similar triangles, labeled XYZ and QPR. - XYZ has angles with the following measurements: - X = 56° - Y and Z are not specified but are marked to imply similarity to QPR. - QPR includes: - Angle at Q measuring the same as angle X from triangle XYZ which is 56° - Side QR measures 6 cm. --- - This content is designed for educational purposes to assist in understanding the relationships in similar triangles and the properties of angles and sides.
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