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Question

The two polar coordinates are (44,150o) and (44,30o). Find the distance between them.

A
442
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B
223
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C
443
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D
513
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Solution

The correct option is D 443
Given two polar coordinates
A(44,150°) ,B(44,30°)
When they are transferred to rectangular coordinates.
From (r,θ)(x,y)
By using cosine function for x
cos(150°)=x44x=44cos150=38.11
By using sine function for y,
sin(150)=y44y=44sin(150)=22
The point A(44,150) A(-38.11,22)
For B(44,30)
By cosine function for x
cos30=x44x=44cos30=38.11
By sine function for y
sin30=y44y=44sin30=22
Distance of AB
(38.11+38.11)2+(2222)2=76.22

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