<u>Answer:</u>
a) Cartesian coordinates of (2.50 m, 30.0°) = (2.17.1.25)
Cartesian coordinates of (3.80 m, 120.0°) = (-1.90.3.29)
b) Distance between (2.17.1.25) and (-1.90.3.29) = 4.55 meter.
<u>Explanation:</u>
Points in polar coordinates = (2.50 m, 30.0°) and (3.80 m, 120.0°)
(2.50 m, 30.0°) = (2.50*cos 30, 2.50*sin 30) = (2.17.1.25)
(3.80 m, 120.0°) = (3.80*cos 120, 3.80*sin 120) = (-1.90.3.29)
a) Cartesian coordinates of (2.50 m, 30.0°) = (2.17.1.25)
Cartesian coordinates of (3.80 m, 120.0°) = (-1.90.3.29)
b) We have distance between (a,b) and (c,d) by distance formula ![\sqrt{(c-a)^2+(d-b)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28c-a%29%5E2%2B%28d-b%29%5E2%7D)
So distance between (2.17.1.25) and (-1.90.3.29) = ![\sqrt{(-1.9-2.17)^2+(3.29-1.25)^2}=\sqrt{20.7265}=4.55 meter](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1.9-2.17%29%5E2%2B%283.29-1.25%29%5E2%7D%3D%5Csqrt%7B20.7265%7D%3D4.55%20meter)
Distance between (2.17.1.25) and (-1.90.3.29) = 4.55 meter.