What is the distance between the following polar coordinates?: <mstyle displaystyle="true">

Kendrick Hampton

Kendrick Hampton

Answered question

2022-06-08

What is the distance between the following polar coordinates?: ( 2 , π 4 ) , ( 5 , 5 π 8 )

Answer & Explanation

ejigaboo8y

ejigaboo8y

Beginner2022-06-09Added 29 answers

Step 1
If we denote ( 2 , π 4 ) by A, ( 5 , 5 π 8 ) by B and the origin by O, and the angle A O B by θ , Then:
θ = 5 π 8 - π 4 = 3 π 8
If we apply the cosine rule:
a 2 = b 2 + c 2 - 2 a b cos A
Then we get:
( A B ) 2 = ( O A ) 2 + ( O B ) 2 - 2 ( O A ) ( O B ) cos θ
= ( 2 ) 2 + ( 5 ) 2 - 2 ( 2 ) ( 5 ) cos ( 3 π 8 )
= 4 + 25 - 20 cos ( 3 π 8 )
= 29 - 20 cos ( 3 π 8 )
= 21.34633 ...
A B = 4.629209

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