Question

Please help and show all work thank you very much.

Answer 1

To express this vector as an ordered pair, we have to find the magnitudes of the x and y direction of the vector.

We are already given the angle of the vector and the magnitude of the vector. If we imagine this as a right triangle, we can use the sine and cosine to find the magnitudes of the x and y direction for the vector.

y direction magnitude:
$54 \sin{69} \approx 50.4$

x direction magnitude:
$54 \cos{69} \approx 19.4$

Ordered pair:
<19.4, 50.4>

I hope this helps! :)