For each of the following, solve for the unknowns. a. b. 16/3 16 212 y. 45° 45 |and y= (Type exact answers, using radicals as needed.) a. x= b. x=and y =D (Type exact answers, using radicals as needed.)

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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### Solving for Unknowns in Right Triangles

**Problem Statement:**
For each of the following, solve for the unknowns.

#### Diagram a:
- Triangle with sides labeled as follows:
  - Hypotenuse: \[16\sqrt{3}\]
  - One leg adjacent to the right angle: 16
  - The other leg adjacent to the right angle labeled as \(y\)
  - Base of the triangle labeled as \(x\)

![Diagram a](diagram_a.png)

**To solve for:** 
- \(x\)
- \(y\)

*Note: Type exact answers using radicals as needed.*

#### Diagram b:
- Triangle with sides labeled as follows:
  - Hypotenuse: \[2\sqrt{2}\]
  - Two angles each measuring \(45^\circ\)
  - One leg adjacent to the right angle labeled as \(y\)
  - Base of the triangle labeled as \(x\)

![Diagram b](diagram_b.png)

**To solve for:**
- \(x\)
- \(y\)

*Note: Type exact answers using radicals as needed.*

**Solution Fields:**
- For diagram a:
  - \(x = \) [ ]
  - \(y = \) [ ]

- For diagram b:
  - \(x = \) [ ]
  - \(y = \) [ ]
Transcribed Image Text:### Solving for Unknowns in Right Triangles **Problem Statement:** For each of the following, solve for the unknowns. #### Diagram a: - Triangle with sides labeled as follows: - Hypotenuse: \[16\sqrt{3}\] - One leg adjacent to the right angle: 16 - The other leg adjacent to the right angle labeled as \(y\) - Base of the triangle labeled as \(x\) ![Diagram a](diagram_a.png) **To solve for:** - \(x\) - \(y\) *Note: Type exact answers using radicals as needed.* #### Diagram b: - Triangle with sides labeled as follows: - Hypotenuse: \[2\sqrt{2}\] - Two angles each measuring \(45^\circ\) - One leg adjacent to the right angle labeled as \(y\) - Base of the triangle labeled as \(x\) ![Diagram b](diagram_b.png) **To solve for:** - \(x\) - \(y\) *Note: Type exact answers using radicals as needed.* **Solution Fields:** - For diagram a: - \(x = \) [ ] - \(y = \) [ ] - For diagram b: - \(x = \) [ ] - \(y = \) [ ]
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