Distance between Two points in Polar Coordinates

Calculus Level 3

If A ( 7 , θ 1 ) A(7,\theta_1) and B ( 10 , θ 2 ) B(10,\theta_2) are two points such that ( θ 1 − θ 2 ) = π 2 (\theta_1-\theta_2)=\dfrac{\pi}{2} , what is the distance between A A and B B ?

17 12 12.207 0.207 3.207

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
May 21, 2016

The distance between the two points A and B with polar coordintes is d = r 1 2 + r 2 2 − 2 r 1 r 2 c o s ( θ 1 − θ 2 ) d=\sqrt{r_1^{2}+r_2^{2}-2r_1r_2cos(\theta_1-\theta_2)} ⟹ \implies

d = 7 2 + 1 0 2 − 2 ∗ 7 ∗ 10 cos ⁡ ( π 2 d=\sqrt{7^{2}+10^{2}-2*7*10\cos(\frac{\pi}{2}} )= 149 = 12.207 \sqrt{149}=12.207

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