What is the distance between the following polar coordinates?:

$(2,\frac{7\pi}{4}),(7,\frac{7\pi}{8})$

$(2,\frac{7\pi}{4}),(7,\frac{7\pi}{8})$

Alissa Hancock
2022-07-07
Answered

What is the distance between the following polar coordinates?:

$(2,\frac{7\pi}{4}),(7,\frac{7\pi}{8})$

$(2,\frac{7\pi}{4}),(7,\frac{7\pi}{8})$

You can still ask an expert for help

Darrell Valencia

Answered 2022-07-08
Author has **10** answers

Step 1

The two points and the origin form a triangle with sides, $a=2,b=7,$,\ b=7, and the angle between them $C=\frac{7\pi}{4}-\frac{7\pi}{8}=\frac{7\pi}{8}$. Therefore, the distance between the two points will be the length of side, c, and we can use the Law of Cosines to find its length:

$c=\sqrt{{a}^{2}+{b}^{2}-2\left(a\right)\left(b\right)\mathrm{cos}\left(C\right)}$

$c=\sqrt{{2}^{2}+{7}^{2}-2\left(2\right)\left(7\right)\mathrm{cos}\left(\frac{7\pi}{8}\right)}$

$c\approx 8.88$

The two points and the origin form a triangle with sides, $a=2,b=7,$,\ b=7, and the angle between them $C=\frac{7\pi}{4}-\frac{7\pi}{8}=\frac{7\pi}{8}$. Therefore, the distance between the two points will be the length of side, c, and we can use the Law of Cosines to find its length:

$c=\sqrt{{a}^{2}+{b}^{2}-2\left(a\right)\left(b\right)\mathrm{cos}\left(C\right)}$

$c=\sqrt{{2}^{2}+{7}^{2}-2\left(2\right)\left(7\right)\mathrm{cos}\left(\frac{7\pi}{8}\right)}$

$c\approx 8.88$

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