Question

PLEASE HELP ME!!!

You and your friend got tricked into helping another friend move stuff from a garage into moving truck. The ramp used is 12 feet long and makes a 36° angle with the horizontal ground. You discover that the incline is just too steep, so you replace the ramp with one that is 32 feet long. What angle does this replacement ramp make with the ground? Round your answer to the nearest tenth of a degree

Answer 1

12.73 Degrees

Explanation:

I'm going to assume some things. The height of the truck is not changing, i.e. the the distance and length of the ramp is but the height stays the same.

We draw our right triangle, see photo

We really only care about finding out what side a is so

`c = (a)/( \sin(x) )`

Note: Let x = A

`12 = (a)/( \sin(36) )`

`12 \sin(36) = a \\ a = 7.05342302750`

`\sin(x) = ( (opp)/(hyp) ) \\ \sin(x) = ( (7.05342302750)/(12) ) \\ = 35.9999 \: degrees`

So, since I stated that height did not change, same process just using 32 for the hypotenuse.

`\sin(x) = ( (opp)/(hyp) ) \\ \sin(x) = ( (7.05342302750)/(32) ) \\ = 12.73367164 \: \: degrees`