Answer :
To determine the angle of incline that the ramp forms with the ground, we can use trigonometric functions. Let's follow a step-by-step solution:
1. Identify the given data:
- The length of the ramp (hypotenuse) is 21.0 meters.
- The height of the ramp (opposite side) is 7.0 meters.
2. Apply the trigonometric function to find the angle:
- Use the tangent function, which relates the opposite side and the adjacent side of a right triangle. In this case, the adjacent side can be interpreted as the horizontal distance along the ground that the ramp spans.
- The tangent of the angle ([tex]\(\theta\)[/tex]) is given by:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
3. Calculate the angle:
- To find the angle [tex]\(\theta\)[/tex], we can use the inverse tangent (arctangent) function:
[tex]\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \][/tex]
- Here, the opposite side is 7.0 meters and the adjacent side is 21.0 meters.
[tex]\[ \theta = \arctan\left(\frac{7.0}{21.0}\right) \][/tex]
4. Convert the angle from radians to degrees for better understanding:
- The angle in radians is approximately 0.32175 radians.
- Converting radians to degrees using the conversion factor [tex]\(180/\pi\)[/tex]:
[tex]\[ \theta \approx 18.4349 \text{ degrees} \][/tex]
5. Round the angle to the nearest degree:
- When rounded to the nearest degree, [tex]\(\theta\)[/tex] is approximately [tex]\(18\)[/tex] degrees.
Therefore, the angle of incline that the ramp forms with the ground is approximately [tex]\(18\)[/tex] degrees.
1. Identify the given data:
- The length of the ramp (hypotenuse) is 21.0 meters.
- The height of the ramp (opposite side) is 7.0 meters.
2. Apply the trigonometric function to find the angle:
- Use the tangent function, which relates the opposite side and the adjacent side of a right triangle. In this case, the adjacent side can be interpreted as the horizontal distance along the ground that the ramp spans.
- The tangent of the angle ([tex]\(\theta\)[/tex]) is given by:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
3. Calculate the angle:
- To find the angle [tex]\(\theta\)[/tex], we can use the inverse tangent (arctangent) function:
[tex]\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \][/tex]
- Here, the opposite side is 7.0 meters and the adjacent side is 21.0 meters.
[tex]\[ \theta = \arctan\left(\frac{7.0}{21.0}\right) \][/tex]
4. Convert the angle from radians to degrees for better understanding:
- The angle in radians is approximately 0.32175 radians.
- Converting radians to degrees using the conversion factor [tex]\(180/\pi\)[/tex]:
[tex]\[ \theta \approx 18.4349 \text{ degrees} \][/tex]
5. Round the angle to the nearest degree:
- When rounded to the nearest degree, [tex]\(\theta\)[/tex] is approximately [tex]\(18\)[/tex] degrees.
Therefore, the angle of incline that the ramp forms with the ground is approximately [tex]\(18\)[/tex] degrees.
