A right triangle is shown below with the dimensions given in units. y O A) 7.6 Which measurement is closest to the value of y in units? O B) 9.3 O C) 9.7 12 O D) 14.8 51°
A right triangle is shown below with the dimensions given in units. y O A) 7.6 Which measurement is closest to the value of y in units? O B) 9.3 O C) 9.7 12 O D) 14.8 51°
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,...
Related questions
Question
![## Understanding Right Triangles
### Problem Statement:
A right triangle is shown below with the dimensions given in units.
### Diagram Explanation:
The diagram depicts a right triangle with one of its angles as \(51^\circ\). The side opposite the right angle (known as the hypotenuse) is labeled as \(12\) units. The side opposite to the \(51^\circ\) angle is labeled as \(y\).
The triangle can be visually summarized as:
- The hypotenuse = \(12\) units
- An angle = \(51^\circ\)
- The side opposite the \(51^\circ\) angle is \(y\)
- The right angle
### Question:
Which measurement is closest to the value of \(y\) in units?
### Answer Choices:
- A) \(7.6\)
- B) \(9.3\)
- C) \(9.7\)
- D) \(14.8\)
Use trigonometric relationships to find the length of \(y\). The sine of an angle in a right triangle is defined as the length of the opposite side divided by the hypotenuse:
\[
\sin(51^\circ) = \frac{y}{12}
\]
Solving for \(y\):
\[
y = 12 \cdot \sin(51^\circ)
\]
### Calculation:
Calculating \( \sin(51^\circ) \approx 0.777 \):
\[
y \approx 12 \cdot 0.777 = 9.324 \text{ units}
\]
Thus, the closest measurement to the value of \(y\) is:
- B) \(9.3\)
This problem utilizes the concepts of right triangles and trigonometric ratios to find the unknown side length.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa368cff4-d7f5-43b5-a63c-d2db6a2e2ef7%2F4e6f78b6-8400-4522-b06b-e5b356c9cafe%2Fw6x20h_processed.png&w=3840&q=75)
Transcribed Image Text:## Understanding Right Triangles
### Problem Statement:
A right triangle is shown below with the dimensions given in units.
### Diagram Explanation:
The diagram depicts a right triangle with one of its angles as \(51^\circ\). The side opposite the right angle (known as the hypotenuse) is labeled as \(12\) units. The side opposite to the \(51^\circ\) angle is labeled as \(y\).
The triangle can be visually summarized as:
- The hypotenuse = \(12\) units
- An angle = \(51^\circ\)
- The side opposite the \(51^\circ\) angle is \(y\)
- The right angle
### Question:
Which measurement is closest to the value of \(y\) in units?
### Answer Choices:
- A) \(7.6\)
- B) \(9.3\)
- C) \(9.7\)
- D) \(14.8\)
Use trigonometric relationships to find the length of \(y\). The sine of an angle in a right triangle is defined as the length of the opposite side divided by the hypotenuse:
\[
\sin(51^\circ) = \frac{y}{12}
\]
Solving for \(y\):
\[
y = 12 \cdot \sin(51^\circ)
\]
### Calculation:
Calculating \( \sin(51^\circ) \approx 0.777 \):
\[
y \approx 12 \cdot 0.777 = 9.324 \text{ units}
\]
Thus, the closest measurement to the value of \(y\) is:
- B) \(9.3\)
This problem utilizes the concepts of right triangles and trigonometric ratios to find the unknown side length.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education