## mattishot 2 years ago 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?

1. tcarroll010

|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.

2. mattishot

so sin 6/45?

3. tcarroll010

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.

4. mattishot

okay, i gotcha. i never know when to use what :/

5. tcarroll010

In other words:$\sin x = \frac{ 6 }{ 45 }$

6. tcarroll010

$x = \sin^{-1} \frac{ 6 }{ 45 }$

7. tcarroll010

sines go with the angle. Arcsines (inverse sines) go with the ratio of the sides.

8. mattishot

ohhh. alright.

9. tcarroll010

So, to calculate that, you set your calculator to "degrees", type in 6/45, then hit inverse sine.

10. tcarroll010

It will give back the angle whose sine is 6/45. Good luck in all of your studies and thx for the recognition! @mattishot

11. mattishot

Thank you too!

12. tcarroll010

You're very welcome! Have a good rest of the day!

13. mattishot

You as well.