Find the horizontal width of a skateboard ramp if it has height 3 ft and a 20-degree incline. Round your answer to the nearest hundredth of a foot.
Find the horizontal width of a skateboard ramp if it has height 3 ft and a 20-degree incline. Round your answer to the nearest hundredth of a foot.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![The problem is to find the horizontal width of a skateboard ramp given the height and angle of incline.
**Problem**:
Find the horizontal width of a skateboard ramp if it has a height of 3 feet and a 20-degree incline. Round your answer to the nearest hundredth of a foot.
**Solution**:
To solve this problem, you can use trigonometry, specifically the tangent function in a right triangle, which relates the angle to the opposite side and adjacent side.
Let's denote:
- The height of the ramp (the vertical side of the right triangle) as \( h = 3 \) ft.
- The angle of the ramp incline as \( \theta = 20^\circ \).
- The horizontal width (the length of the adjacent side to the angle), which we need to find, as \( w \).
Using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
\[ \tan(20^\circ) = \frac{3}{w} \]
Solving for \( w \):
\[ w = \frac{3}{\tan(20^\circ)} \]
Using a calculator to find \( \tan(20^\circ) \approx 0.364 \):
\[ w \approx \frac{3}{0.364} \]
\[ w \approx 8.24 \]
Hence, the horizontal width of the ramp is approximately 8.24 feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2Fc2c82c81-efc9-46ab-9e01-e12200818bf0%2Fygr99oi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem is to find the horizontal width of a skateboard ramp given the height and angle of incline.
**Problem**:
Find the horizontal width of a skateboard ramp if it has a height of 3 feet and a 20-degree incline. Round your answer to the nearest hundredth of a foot.
**Solution**:
To solve this problem, you can use trigonometry, specifically the tangent function in a right triangle, which relates the angle to the opposite side and adjacent side.
Let's denote:
- The height of the ramp (the vertical side of the right triangle) as \( h = 3 \) ft.
- The angle of the ramp incline as \( \theta = 20^\circ \).
- The horizontal width (the length of the adjacent side to the angle), which we need to find, as \( w \).
Using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
\[ \tan(20^\circ) = \frac{3}{w} \]
Solving for \( w \):
\[ w = \frac{3}{\tan(20^\circ)} \]
Using a calculator to find \( \tan(20^\circ) \approx 0.364 \):
\[ w \approx \frac{3}{0.364} \]
\[ w \approx 8.24 \]
Hence, the horizontal width of the ramp is approximately 8.24 feet.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
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, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning