Question

Find the distance between ($3$, ${60}^o$) and ($5$,${145}^o$).

• A. $6.5$ units
• B. $5.6$ units
• C. $3.5$ units
• D. $6.3$ units

Answer 1

Answer: (B)

$5.6$ units

Distance formula in polar coordinate is given by:

$d=\sqrt{(r_1^2+r_2^2-2r_1{r}_2\cos (\alpha -\beta \left)\right)}$

$d=\sqrt{(5^2+3^2-2\times 5\times 3\cos (145°-60°\left)\right)}$

$=\sqrt{(}25+9-30COS85°)$

$=\sqrt{(}34-30\times \left(.087\right))$

$=\sqrt{(}34-2.61)=\sqrt{(}31.4)=5.6$