If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground? Round your answer to one decimal place. The ramp makes an angle of Number degrees with the ground.
If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground? Round your answer to one decimal place. The ramp makes an angle of Number degrees with the ground.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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![**Problem Description:**
**Title:** Calculating the Angle of a Loading Ramp
**Question:**
If a loading ramp is placed next to a truck at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground?
**Instructions:**
Round your answer to one decimal place.
**Answer Input:**
The ramp makes an angle of ___ degrees with the ground.
**Explanation:**
To solve for the angle that the ramp makes with the ground, you can use trigonometric principles, specifically the sine function. Given the ramp forms a right triangle with:
- The height (opposite side to the angle) = 2 feet
- The ramp length (hypotenuse) = 20 feet.
The sine of the angle θ is given by:
\[ \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{2}{20} = 0.1 \]
To find the angle, take the inverse sine (arcsine) of 0.1:
\[ \theta = \arcsin(0.1) \]
Using a calculator or trigonometric table, determine the angle θ and round the result to one decimal place for your answer.
---
In the input field provided, enter the calculated angle to see if you are correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b256bb6-7576-446c-ac07-c5d4136bf792%2F3728dfca-5f81-4a26-bf3c-dae0db0a285d%2Farq4ap_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
**Title:** Calculating the Angle of a Loading Ramp
**Question:**
If a loading ramp is placed next to a truck at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground?
**Instructions:**
Round your answer to one decimal place.
**Answer Input:**
The ramp makes an angle of ___ degrees with the ground.
**Explanation:**
To solve for the angle that the ramp makes with the ground, you can use trigonometric principles, specifically the sine function. Given the ramp forms a right triangle with:
- The height (opposite side to the angle) = 2 feet
- The ramp length (hypotenuse) = 20 feet.
The sine of the angle θ is given by:
\[ \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{2}{20} = 0.1 \]
To find the angle, take the inverse sine (arcsine) of 0.1:
\[ \theta = \arcsin(0.1) \]
Using a calculator or trigonometric table, determine the angle θ and round the result to one decimal place for your answer.
---
In the input field provided, enter the calculated angle to see if you are correct.
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