Problem

If a loading ramp is placed next to a truck, at a height of 6 feet, and the inclined portion of the ramp is 21 feet long, what angle (in degrees) does the ramp make with the ground? Round your answer to one-tenth of a degree.

Solution

Step 1 :Given: Opposite side (height) = 6 feet, Hypotenuse (length of ramp) = 21 feet

Step 2 :Use sine function: \(\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\)

Step 3 :Plug in values: \(\sin(\text{angle}) = \frac{6}{21}\)

Step 4 :Find the angle in radians: \(\text{angle}_\text{radians} = \arcsin(\frac{6}{21})\)

Step 5 :Convert radians to degrees: \(\text{angle}_\text{degrees} = \text{angle}_\text{radians} \times \frac{180}{\pi}\)

Step 6 :Round the angle to one-tenth of a degree: \(\text{rounded}_\text{angle} = 16.6\)

Step 7 :\(\boxed{\text{Final Answer: The angle the ramp makes with the ground is 16.6 degrees}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/15973/

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