Find the length of the missing leg of a right triangle whose hypotenuse measures 15 cm and whose other leg measures 13 cm. If necessary, round your answer to the nearest tenth. 3.2 cm 7.9 cm 7.5 cm 8.6 cm D
Find the length of the missing leg of a right triangle whose hypotenuse measures 15 cm and whose other leg measures 13 cm. If necessary, round your answer to the nearest tenth. 3.2 cm 7.9 cm 7.5 cm 8.6 cm D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Finding the Missing Leg of a Right Triangle**
To find the length of the missing leg \(a\) in a right triangle where the hypotenuse \(c\) measures 15 cm and the other leg \(b\) measures 13 cm, apply the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Given \( c = 15 \) cm and \( b = 13 \) cm, substitute these values into the equation:
\[ 15^2 = a^2 + 13^2 \]
\[ 225 = a^2 + 169 \]
\[ 225 - 169 = a^2 \]
\[ 56 = a^2 \]
\[ a = \sqrt{56} \]
\[ a \approx 7.5 \, \text{cm} \]
Therefore, the length of the missing leg is approximately \( 7.5 \) cm.
On this basis, the correct answer is:
* 3.2 cm
* 7.9 cm
* 7.5 cm
* 8.6 cm
Option **7.5 cm** is correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af3b856-d446-4ff7-a63e-89e70c8da553%2F012f6922-8641-4f2c-b966-9212f88fbc2d%2F3a6krev_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Missing Leg of a Right Triangle**
To find the length of the missing leg \(a\) in a right triangle where the hypotenuse \(c\) measures 15 cm and the other leg \(b\) measures 13 cm, apply the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Given \( c = 15 \) cm and \( b = 13 \) cm, substitute these values into the equation:
\[ 15^2 = a^2 + 13^2 \]
\[ 225 = a^2 + 169 \]
\[ 225 - 169 = a^2 \]
\[ 56 = a^2 \]
\[ a = \sqrt{56} \]
\[ a \approx 7.5 \, \text{cm} \]
Therefore, the length of the missing leg is approximately \( 7.5 \) cm.
On this basis, the correct answer is:
* 3.2 cm
* 7.9 cm
* 7.5 cm
* 8.6 cm
Option **7.5 cm** is correct.
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