Question

Question #95835

Answer 1

Cartesian coordinates of point A is `(2.17,1.25)`
Cartesian coordinates of point B is `(-1.9,3.29)`
Distance between them is `4.55` m.

Explanation:

Polar coordinates of point A is `r_1=2.50m , theta_1=30^0`

Polar coordinates of point B is `r_2=3.80m , theta_2=120^0`

Cartesian coordinates of point A is `x_1=r_1 cos theta_1`

or `x_1= 2.5 cos 30 = 2.165, y_1=r_1 sin theta` or

`y_1=2.5 sin 30 =1.25 :.` Cartesian coordinates of

point A is `(x_1,y_1) or (2.17,1.25)`

Cartesian coordinates of point B is `x_2=r_2 cos theta_2`

or `x_2= 3.8 cos 120 = -1.9, y_2=r_2 sin theta_2` or

`y_2=3.8 sin 120=3.29`. Cartesian coordinates of

point B is `(x_2,y_2) or (-1.9,3.29)`

Distance between them `D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2`

`D= sqrt ((2.17+1.9)^2+(1.25-3.29)^2) = 4.55` m