Question

A line 10cm long has a direction specified by the polar angle 100`. If one end is at (7,160`) find the polar coordinates of the other end.

Answer 1

Hi .. how are you ? hop you are fine .. lets Trying your Q.
first of all we have to understand you Q.
you have line that (10,100') .. first point of it (7,160') and you need to find the other point.

That is mean ... you have to find draw (10,100) from point (7,160') then the end will be easy to calculate .
The figure below showing that .



to find x1 , the angle of the 7 length lineis 160 degree so the rest of the angle = 20 degree on the other side:

\[\huge{x _{1} = -7\cos 20=-6.577} \]
\[\huge {x _{2}= -10 \cos80 = - 1.736 }\]
x= x1+x2=3.313 unit

\[\huge {y_{1}=7 \sin 20= 2.394 }\]
\[\huge {y_{2}=10 \sin 80 = 9.848}\]
Y= y1+y2 = 12.242 unit

\[\huge {r=\sqrt{x^{2}+y^{2}}}\]
\[\huge {r=\sqrt{8.313^{2}+12.242^{2}}}=14.798\]

\[\huge {\theta = 180 - \tan^{-1} \frac{y}{x}}=180-55.82=124.178\]

(r,theta)
\[\huge \text { (14.798,124.178')}\]