Find the length of the missing leg of a right triangle whose hypotenuse measures 15.4 cm and whose other leg measures 6.3 cm. If necessary, round your answer to the nearest tenth. 20.5 cm 15.7 cm 14.1 cm 13.2 cm
Find the length of the missing leg of a right triangle whose hypotenuse measures 15.4 cm and whose other leg measures 6.3 cm. If necessary, round your answer to the nearest tenth. 20.5 cm 15.7 cm 14.1 cm 13.2 cm
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**
*Problem Statement:*
Find the length of the missing leg of a right triangle whose hypotenuse measures 15.4 cm and whose other leg measures 6.3 cm. If necessary, round your answer to the nearest tenth.
*Options:*
- 20.5 cm
- 15.7 cm
- 14.1 cm
- 13.2 cm
**Explanation:**
To find the length of the missing leg, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two legs (a and b). Mathematically, this can be represented as:
\[ c^2 = a^2 + b^2 \]
Given:
\[ c = 15.4 \, \text{cm} \]
\[ a = 6.3 \, \text{cm} \]
We need to find \( b \).
\[ (15.4)^2 = (6.3)^2 + b^2 \]
\[ 237.16 = 39.69 + b^2 \]
\[ b^2 = 237.16 - 39.69 \]
\[ b^2 = 197.47 \]
\[ b = \sqrt{197.47} \]
\[ b \approx 14.1 \, \text{cm} \]
Therefore, the length of the missing leg is approximately 14.1 cm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af3b856-d446-4ff7-a63e-89e70c8da553%2Fa7551373-0443-46f1-838c-3abc5e4bdc29%2Fak15r6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Missing Leg of a Right Triangle**
*Problem Statement:*
Find the length of the missing leg of a right triangle whose hypotenuse measures 15.4 cm and whose other leg measures 6.3 cm. If necessary, round your answer to the nearest tenth.
*Options:*
- 20.5 cm
- 15.7 cm
- 14.1 cm
- 13.2 cm
**Explanation:**
To find the length of the missing leg, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two legs (a and b). Mathematically, this can be represented as:
\[ c^2 = a^2 + b^2 \]
Given:
\[ c = 15.4 \, \text{cm} \]
\[ a = 6.3 \, \text{cm} \]
We need to find \( b \).
\[ (15.4)^2 = (6.3)^2 + b^2 \]
\[ 237.16 = 39.69 + b^2 \]
\[ b^2 = 237.16 - 39.69 \]
\[ b^2 = 197.47 \]
\[ b = \sqrt{197.47} \]
\[ b \approx 14.1 \, \text{cm} \]
Therefore, the length of the missing leg is approximately 14.1 cm.
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