If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 20 feet, what angle does the ramp make with the ground? Round to 2 decimal places.
If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 20 feet, what angle does the ramp make with the ground? Round to 2 decimal places.
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°.
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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
![**Problem:**
If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 20 feet, what angle does the ramp make with the ground? Round to 2 decimal places.
**Answer box:**
\[ \boxed{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\,^\circ \]
In this problem, you are given a right triangle where:
- The height of the ramp (opposite side) is 4 feet.
- The length of the ramp (hypotenuse) is 20 feet.
You need to calculate the angle the ramp makes with the ground.
Use the sine function:
\[ \sin{\theta} = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{4}{20} = 0.2 \]
Then find the angle \( \theta \) using the inverse sine function:
\[ \theta = \sin^{-1}(0.2) \approx 11.54^\circ \]
So, the angle the ramp makes with the ground is approximately \( 11.54^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F416064f9-c57b-46ee-9b50-14b257515654%2F72a12645-6632-46a3-86cd-83a190e80e52%2Fx4ldm9.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 20 feet, what angle does the ramp make with the ground? Round to 2 decimal places.
**Answer box:**
\[ \boxed{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\,^\circ \]
In this problem, you are given a right triangle where:
- The height of the ramp (opposite side) is 4 feet.
- The length of the ramp (hypotenuse) is 20 feet.
You need to calculate the angle the ramp makes with the ground.
Use the sine function:
\[ \sin{\theta} = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{4}{20} = 0.2 \]
Then find the angle \( \theta \) using the inverse sine function:
\[ \theta = \sin^{-1}(0.2) \approx 11.54^\circ \]
So, the angle the ramp makes with the ground is approximately \( 11.54^\circ \).
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