Question

The two polar coordinates are $(44,{150}^o)$ and $(44,{30}^o)$. Find the distance between them.

• A. $44\sqrt{2}$
• B. $22\sqrt{3}$
• C. $44\sqrt{3}$
• D. $51\sqrt{3}$

Answer 1

Answer: (C)

$44\sqrt{3}$

Given two polar coordinates

$A(44,150°)$ ,$B(44,30°)$

When they are transferred to rectangular coordinates.

From $(r,\theta )\to (x,y)$

By using cosine function for $x$

$\Rightarrow \cos \left(150°\right)=\frac{x}{44}\therefore x=44\cos 150=-38.11$

By using sine function for y,

$\sin \left(150\right)=\frac{y}{44}\Rightarrow y=44\sin \left(150\right)=22$

$\therefore$The point $A(44,150)$ $\to$ A(-38.11,22)

For $B(44,30)$

By cosine function for $x$

$\cos 30=\frac{x}{44}\Rightarrow x=44\cos 30=38.11$

By sine function for $y$

$\sin 30=\frac{y}{44}\Rightarrow y=44\sin 30=22$

$\therefore$ Distance of AB

$\sqrt{(38.11+38.11{)}^2+(22-22{)}^2}=76.22$