K 59 m 32⁰ 50 m Submit meters 58⁰ J AKIJATUV. What is UV? 31 m I U T

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter2: Equations And Inequalities
Section: Chapter Questions
Problem 4PT: Find the exact distance between (5,3)and(2,8) . Find the coordinates of the midpoint of the line...
Question
### Geometry Problem: Solving for Side Length in Similar Triangles

#### Problem Statement:
Given two triangles \( \triangle KIJ \) and \( \triangle TUV \) are similar. Determine the length of side \( UV \).

#### Diagrams:

1. **Triangle \( \triangle KIJ \):**
   - Right triangle with:
     - \( KI = 50 \) meters
     - \( IJ = 31 \) meters
     - \( JK = 59 \) meters
   - Angles:
     - \( \angle KIJ = 32^\circ \)
     - \( \angle IJK = 58^\circ \)
     - \( \angle I = 90^\circ \)

2. **Triangle \( \triangle TUV \):**
   - The triangle is similar to \( \triangle KIJ \).
   - Sides \( TU \), \( UV \), and \( VT \) are unknown.
   
#### Question:
Find the length of \( UV \).

#### Solution Input:
An input box is provided to enter the length of \( UV \) in meters.

#### Additional Information:
- The problem is displayed on a digital platform, using an educational interface.
- The submit button is available to check the answers.
- Property of Garden Grove USD, barcode tag, and laptop details are visible but unrelated to the geometric problem.

This problem requires understanding of triangle similarity and proportional relationships to solve for unknown side lengths.
Transcribed Image Text:### Geometry Problem: Solving for Side Length in Similar Triangles #### Problem Statement: Given two triangles \( \triangle KIJ \) and \( \triangle TUV \) are similar. Determine the length of side \( UV \). #### Diagrams: 1. **Triangle \( \triangle KIJ \):** - Right triangle with: - \( KI = 50 \) meters - \( IJ = 31 \) meters - \( JK = 59 \) meters - Angles: - \( \angle KIJ = 32^\circ \) - \( \angle IJK = 58^\circ \) - \( \angle I = 90^\circ \) 2. **Triangle \( \triangle TUV \):** - The triangle is similar to \( \triangle KIJ \). - Sides \( TU \), \( UV \), and \( VT \) are unknown. #### Question: Find the length of \( UV \). #### Solution Input: An input box is provided to enter the length of \( UV \) in meters. #### Additional Information: - The problem is displayed on a digital platform, using an educational interface. - The submit button is available to check the answers. - Property of Garden Grove USD, barcode tag, and laptop details are visible but unrelated to the geometric problem. This problem requires understanding of triangle similarity and proportional relationships to solve for unknown side lengths.
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