Using scissors to cut a rectangular piece of paper from one corner ro the opposite corner. The cut is 36 cm long and makes a 34 degree angle to the uncut edge. How many cm long is the paper (from the corner where he started the cut?

sin34 = y/36

y = 36sin34 = appr 20.13

cos34 = x/36
x = 36cos34 = appr. 29.85

the paper was 20.13 cm by 29.85 cm

check:
20.13^2 + 29.85^2 = 1296.23
36^2 = 1296 , good enough using 2 decimals

Find the distance of the point p(6,-6) from the origin.

To find the length of the paper from the starting corner, we can use trigonometry. Let's call the length of the paper "L."

We know that the cut is 36 cm long and makes a 34-degree angle with the uncut edge. We can use these values to form a right triangle.

In this triangle, the cut length (36 cm) is the hypotenuse of the triangle, and the adjacent side is the length of the paper (L). We have the angle between the hypotenuse and the adjacent side.

Using the cosine function, we can write:

cos(34 degrees) = L / 36 cm

Now, we can solve for L:

L = 36 cm * cos(34 degrees)

Using a calculator or software, we can find that cos(34 degrees) ≈ 0.829
Therefore:

L ≈ 36 cm * 0.829 ≈ 29.864 cm

So, the length of the paper from the corner where he started the cut is approximately 29.864 cm.