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

Alissa Hancock 2022-07-07 Answered
What is the distance between the following polar coordinates?:
( 2 , 7 π 4 ) , ( 7 , 7 π 8 )
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Answers (1)

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 = 7 π 4 - 7 π 8 = 7 π 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 = a 2 + b 2 - 2 ( a ) ( b ) cos ( C )
c = 2 2 + 7 2 - 2 ( 2 ) ( 7 ) cos ( 7 π 8 )
c 8.88
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