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If the perimeter of the sector shown in the figure is 18, with radius 4. What is the angle of the sector in radians?

 

 May 16, 2020
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The perimeter of the sector consists of the two radii and the arc.

The two radii (together) have a length of 8.

This leaves  18 - 8  =  10 for the length of the arc.

 

Now, we need to find the circumference of the circle:  C  =  2·pi·r  =  2·pi·4  =  25.1327  (approximately).

 

Radians / 2pi  =  arc length / circumference

Radians / 2pi  =  10 / 25.1327   =  0.3979  (approximately)

Radians =  0.3979 x 2pi  =  0.796pi  =  2.5   (approximately)

 May 16, 2020
edited by geno3141  May 16, 2020

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