A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long, how tall is th- mast? Round to the nearest tenth of a foot. 15 16 17 18 19 20 21 22 23 DELL
A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long, how tall is th- mast? Round to the nearest tenth of a foot. 15 16 17 18 19 20 21 22 23 DELL
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
Related questions
Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![### Understanding Right-Angle Triangles on a Sailboat
#### Problem Statement
A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long, how tall is the mast? Round to the nearest tenth of a foot.
#### Explanation and Solution
In this problem, we can use the Pythagorean theorem to determine the height of the mast. The Pythagorean theorem states that in a right-angled triangle:
\[ a^2 + b^2 = c^2 \]
- \( c \) represents the hypotenuse (the rope in this case, 28 feet).
- \( a \) represents one leg of the triangle (the distance from the mast, 19 feet).
- \( b \) represents the other leg of the triangle (the height of the mast, which we need to find).
Given:
- Hypotenuse, \( c = 28 \) feet
- One leg, \( a = 19 \) feet
We need to find \( b \) (height of the mast).
From the Pythagorean theorem:
\[ 19^2 + b^2 = 28^2 \]
\[ 361 + b^2 = 784 \]
Subtract 361 from both sides:
\[ b^2 = 784 - 361 \]
\[ b^2 = 423 \]
Take the square root of both sides:
\[ b = \sqrt{423} \approx 20.6 \]
So, the height of the mast is approximately 20.6 feet, rounded to the nearest tenth of a foot.
#### Visual Representation
In the image, there is a diagram of a sailboat with a right-angled triangle formed by the mast, the horizontal distance, and the rope. This helps visualize the problem and apply the Pythagorean theorem correctly.
---
Note: It is essential to ensure accuracy in rounding and understanding the geometric principles involved in solving such real-world problems using mathematical concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab545a03-1d39-4874-800c-bed9ffa7318e%2F251dc6be-e3f2-47f4-92f7-8ce56938ab72%2Fxp7o9am_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Right-Angle Triangles on a Sailboat
#### Problem Statement
A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long, how tall is the mast? Round to the nearest tenth of a foot.
#### Explanation and Solution
In this problem, we can use the Pythagorean theorem to determine the height of the mast. The Pythagorean theorem states that in a right-angled triangle:
\[ a^2 + b^2 = c^2 \]
- \( c \) represents the hypotenuse (the rope in this case, 28 feet).
- \( a \) represents one leg of the triangle (the distance from the mast, 19 feet).
- \( b \) represents the other leg of the triangle (the height of the mast, which we need to find).
Given:
- Hypotenuse, \( c = 28 \) feet
- One leg, \( a = 19 \) feet
We need to find \( b \) (height of the mast).
From the Pythagorean theorem:
\[ 19^2 + b^2 = 28^2 \]
\[ 361 + b^2 = 784 \]
Subtract 361 from both sides:
\[ b^2 = 784 - 361 \]
\[ b^2 = 423 \]
Take the square root of both sides:
\[ b = \sqrt{423} \approx 20.6 \]
So, the height of the mast is approximately 20.6 feet, rounded to the nearest tenth of a foot.
#### Visual Representation
In the image, there is a diagram of a sailboat with a right-angled triangle formed by the mast, the horizontal distance, and the rope. This helps visualize the problem and apply the Pythagorean theorem correctly.
---
Note: It is essential to ensure accuracy in rounding and understanding the geometric principles involved in solving such real-world problems using mathematical concepts.
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 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning