Question

question no 3
» topic :- C. geometry

thanks and all the best

Answer 1

This is my answer if u r not satisfied then again report.
Solved by my teacher.

Answer 2

Given,

First Coordinate = (3 , π/4)

Second  coordinates = (7, 5π/4)

We know that, distance between two polar  coordinates (r₁,Ф₁) and  (r₂,Ф₂) is ,

$d=\sqrt{r_1^{2}+r_2^{2}-2r_1r_2\cos(\theta _1-\theta _2)}$

Here,

r₁  = 3

r₂ = 7

Ф₁ = π/4

Ф₂ =  5π/4

Hence,

$d=\sqrt{r_1^{2}+r_2^{2}-2r_1r_2\cos(\theta _1-\theta _2)}\\\\d=\sqrt{3^{2}+7^{2}-2\times3\times7\cos(\frac{\pi}{4}-\frac{5\pi}4})}\\\\d=\sqrt{9+49-42\cos(\frac{-4\pi}{4})}\\\\d=\sqrt{58-42\cos\pi}}\\\\d=\sqrt{58+42}\\\\d=\sqrt{100}\\\\d=10\;units$