What are the magnitudes of the horizontal and vertical components of a vector that is 100 units long...?

Question

What are the magnitudes of the horizontal and vertical components of a vector that is 100 units long, and oriented at 45 degree?

When you answer the question, please also explain WHY, because I don’t just want the answer, I want to learn also =)

Answer 1

To find the orthagional components of the vector, start with the start of the vector and draw a vertical and horizontal line from that point. Now go to the "tip" of the vector and draw a horizontal line from the tip to the vertical line, and a vertical line from the tip of the horizontal line. Now you will have a rectangular "box" with the vector as a diagional.
From the triginometry of right triangles, the horizontal component is 100* cos 45, and the vertical component is 100 * sin 45. At 45 deg, both trig functions are 0.5sqrt(2) or 0.707 (appx).
So each component would be 70.7 units long.