Question

Find the distance between ($9$,${45}^o$) and ($4$,${70}^o$)

• A. $3.16$ units
• B. $5.16$ units
• C. $5.64$ units
• D. None of these

Answer 1

Answer: (C)

$5.64$ units

Distance formula in polar coordinate is given by:

$d=\sqrt{(r_1^2+r_2^2-2r_1{r}_{2}cos(a-b\left)\right)}$

$d=\sqrt{(4^2+9^2-2\times 4\times 9\cos (70°-45°\left)\right)}$

$=\sqrt{(16+81-72\cos 25°)}$

$=\sqrt{(97-72\times (.906\left)\right)}$

$=\sqrt{(97-65.2)}=\sqrt{\left(31.8\right)}=5.64$