Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem:**
Calculate the length of side \( p \) to one decimal place in the right triangle \( \triangle PQR \) where \( r = 9 \) and \( q = 15 \).
**Choices:**
- A. 12.0
- B. 17.5
- C. 144.0
- D. 306.0
**Solution:**
Given:
- \( r = 9 \)
- \( q = 15 \)
We will use the Pythagorean theorem to find \( p \). The Pythagorean theorem states:
\[ p^2 + r^2 = q^2 \]
Substitute the values given:
\[ p^2 + 9^2 = 15^2 \]
\[ p^2 + 81 = 225 \]
Subtract 81 from both sides to solve for \( p^2 \):
\[ p^2 = 225 - 81 \]
\[ p^2 = 144 \]
Taking the square root of both sides to find \( p \):
\[ p = \sqrt{144} \]
\[ p = 12 \]
Thus, the length of side \( p \) is 12.0 when rounded to one decimal place.
**Correct Answer:**
- A. 12.0
**Explanation of Diagram:**
The diagram shows a right triangle \( \triangle PQR \). In the diagram:
- \( \angle Q \) is the right angle.
- The length \( q \) (which is the hypotenuse) is given as 15.
- The length \( r \) (one of the legs) is given as 9.
- We need to find the length of \( p \) (the other leg).
Annotations in the image include:
- The side opposite the right angle (hypotenuse) labeled as \( 15 \).
- A calculation leading to the determination that \( \sqrt{306} \approx 17.5 \), but this appears to be scribbles and not the correct answer, evident by the scratch-outs and the \( 225 - 81 = 144;\sqrt{144} = 12 \) calculation confirming the correct value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6c4205f-2502-4492-9bc7-9a1cd462e155%2F2a2d8c5f-369d-4682-b6ef-4b352ca705b4%2Fotxxur3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Calculate the length of side \( p \) to one decimal place in the right triangle \( \triangle PQR \) where \( r = 9 \) and \( q = 15 \).
**Choices:**
- A. 12.0
- B. 17.5
- C. 144.0
- D. 306.0
**Solution:**
Given:
- \( r = 9 \)
- \( q = 15 \)
We will use the Pythagorean theorem to find \( p \). The Pythagorean theorem states:
\[ p^2 + r^2 = q^2 \]
Substitute the values given:
\[ p^2 + 9^2 = 15^2 \]
\[ p^2 + 81 = 225 \]
Subtract 81 from both sides to solve for \( p^2 \):
\[ p^2 = 225 - 81 \]
\[ p^2 = 144 \]
Taking the square root of both sides to find \( p \):
\[ p = \sqrt{144} \]
\[ p = 12 \]
Thus, the length of side \( p \) is 12.0 when rounded to one decimal place.
**Correct Answer:**
- A. 12.0
**Explanation of Diagram:**
The diagram shows a right triangle \( \triangle PQR \). In the diagram:
- \( \angle Q \) is the right angle.
- The length \( q \) (which is the hypotenuse) is given as 15.
- The length \( r \) (one of the legs) is given as 9.
- We need to find the length of \( p \) (the other leg).
Annotations in the image include:
- The side opposite the right angle (hypotenuse) labeled as \( 15 \).
- A calculation leading to the determination that \( \sqrt{306} \approx 17.5 \), but this appears to be scribbles and not the correct answer, evident by the scratch-outs and the \( 225 - 81 = 144;\sqrt{144} = 12 \) calculation confirming the correct value.
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