A long ramp that leads to a building entrance is 45 feet. The stairs to the entrance have a vertical height of 6 feet. What is the angle of incline of the ramp?

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A long ramp that leads to a building entrance is 45 feet. The stairs to the entrance have a vertical height of 6 feet. What is the angle of incline of the ramp?

Mathematics
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|dw:1363223850112:dw|In this drawing you can identify the angle "x", the opposite side and the hypotenuse. The angle "x" is that angle whose sine is the measure of the length of opposite side over the measure of the length of the hypotenuse.
so sin 6/45?
Actually, the angle is the arcsin 6/45. It's the inverse sine. You are given the sine. It's the angle is what you are looking for.

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okay, i gotcha. i never know when to use what :/
In other words:\[\sin x = \frac{ 6 }{ 45 }\]
\[x = \sin^{-1} \frac{ 6 }{ 45 }\]
sines go with the angle. Arcsines (inverse sines) go with the ratio of the sides.
ohhh. alright.
So, to calculate that, you set your calculator to "degrees", type in 6/45, then hit inverse sine.
It will give back the angle whose sine is 6/45. Good luck in all of your studies and thx for the recognition! @mattishot
Thank you too!
You're very welcome! Have a good rest of the day!
You as well.

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