A certain television is advertised as a 63-inch TV (the diagonal length). If the height of the TV is 43 inches, how wide is the TV? Round to the nearest tenth of an inch.
A certain television is advertised as a 63-inch TV (the diagonal length). If the height of the TV is 43 inches, how wide is the TV? Round to the nearest tenth of an inch.
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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![**Educational Website Text Transcription**
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### Problem Statement:
A certain television is advertised as a 63-inch TV (the diagonal length). If the height of the TV is 43 inches, how wide is the TV? Round to the nearest tenth of an inch.
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In this lesson, we will use the Pythagorean theorem to solve for the width of the television. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. For our TV problem, the diagonal length is the hypotenuse, and the height and width of the TV are the other two sides of the right triangle.
Given:
- Diagonal length (hypotenuse): 63 inches
- Height: 43 inches
We need to find the width (W).
Using the Pythagorean theorem:
\[ \text{Diagonal}^2 = \text{Height}^2 + \text{Width}^2 \]
First, substitute the known values into the equation:
\[ 63^2 = 43^2 + W^2 \]
Calculate the squares:
\[ 3969 = 1849 + W^2 \]
Isolate the width term:
\[ 3969 - 1849 = W^2 \]
\[ 2120 = W^2 \]
Solve for the width:
\[ W = \sqrt{2120} \]
\[ W \approx 46.0 \]
So, the width of the TV is approximately 46.0 inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08807450-21ed-4e55-84b1-e841f0af059c%2F24181b1d-6dd9-4941-b6b6-00bf767d787c%2F5tfzix5_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Text Transcription**
---
### Problem Statement:
A certain television is advertised as a 63-inch TV (the diagonal length). If the height of the TV is 43 inches, how wide is the TV? Round to the nearest tenth of an inch.
---
In this lesson, we will use the Pythagorean theorem to solve for the width of the television. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. For our TV problem, the diagonal length is the hypotenuse, and the height and width of the TV are the other two sides of the right triangle.
Given:
- Diagonal length (hypotenuse): 63 inches
- Height: 43 inches
We need to find the width (W).
Using the Pythagorean theorem:
\[ \text{Diagonal}^2 = \text{Height}^2 + \text{Width}^2 \]
First, substitute the known values into the equation:
\[ 63^2 = 43^2 + W^2 \]
Calculate the squares:
\[ 3969 = 1849 + W^2 \]
Isolate the width term:
\[ 3969 - 1849 = W^2 \]
\[ 2120 = W^2 \]
Solve for the width:
\[ W = \sqrt{2120} \]
\[ W \approx 46.0 \]
So, the width of the TV is approximately 46.0 inches.
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