A 150-foot-long ramp connects a ground-level parking lot with the entrance of a building. if the entrance is 8 feet above the ground, what angle does the ramp make with the ground. draw the picture
let's see. you have the height and the hypotenuse. The height is opposite the angle where the ramp touches the ground.
Draw a picture in situations like this.
Now, which trig function involves opposite/hypotenuse?
sine
To find the angle that the ramp makes with the ground, we can use trigonometry. Let's draw the picture to better visualize the situation.
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| Building |
|______|
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| Ramp
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|_______________________
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Ground
In this diagram, the ground is at the bottom, and the building is represented by a rectangle. The ramp connects the ground-level parking lot to the entrance of the building, which is 8 feet above the ground.
To find the angle that the ramp makes with the ground, we can use the tangent of the angle, which is defined as the opposite side (the height) divided by the adjacent side (the length of the ramp). In this case, the height is 8 feet, and the length of the ramp is 150 feet.
Therefore, we have:
tan(theta) = opposite/adjacent
tan(theta) = 8/150
Taking the inverse tangent (arctan) of both sides, we can find the angle:
theta = arctan(8/150)
Using a calculator or trigonometric table, you can find that the approximate value of arctan(8/150) is approximately 3.04 degrees.
So, the angle that the ramp makes with the ground is approximately 3.04 degrees.