trigonometry
posted by delwin .
Find the radius of a circle on which a central angle of 3 pie over 2 radians subtends an arc of 60 ft.

First note that a whole circle measures 360 degrees or 2pi radians. The 3/2pi radians is just 3/4 of 2pi, Thus we can say that the length of arc given (the 60 ft) is just 3/4 of the circumference of the circle.
If 60 is just 3/4 of the whole, then 60/(3/4) = 80 ft is the circumference of the circle.
Recall that the circumference of circle is given by
C = 2*pi*r
where r = radius
Substituting,
80 = 2*pi*r
r = 80/(2*pi)
r = 40/pi = 12.74 ft
hope this helps~ :) 
If a central angle theta = 3 pi / 2 then :
Circumference of a circle = 2 * r * pi
Ful circle have 360 ° = 2 pi radians.
Lenght of arc :
L = ( theta / 2 pi ) * 2 * r * pi
L = theta * r = 60
( 3 pi / 2 ) * r = 60 Multiply both sides by 2
3 pi * r = 120 Divide both sides by 3 pi
r = 120 / 3 pi = 40 / pi
Respond to this Question
Similar Questions

trigonometry
please check my answers. 1.Find the area of the sector of a circle. r=11.8cm, thetapi/7 radians I got 31.2cmsquared 2.Find the radius of a circle in which a central angle of pi/6radian determines a sector of area 76square meters. … 
math 30 Trig
A central angle subtends an arc of 35 cm. If the radius of the circle is 12 cm, what is the measure of the central angle? 
maths
an arc of a circle subtends a central angle of 5pi/6 radians.if the radius of the circle measures 10.6cm, determine the approx measure of the arc leanth 
Bobby
Find the length (in cm) of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°. 
math
An angle of 1.8 radians at the center of the circle subtends an arc of length 23.4cm. Find: (a) The radius of the circle (b) The area of the sector enclosed by the arc and the radii. 
Math
Find the radius of the circle if an arc of length 5 ft on the circle subtends a central angle of 135°. (Round your answer to two decimal places.) 
math
find the length of an arc of a circle of radius 5.6 cm which subtends an angle of 60 degrees at the centre of the circle.(take pie as 22 divided by 7.) 
math
Find the radius of the circle if an arc of length 8 ft on the circle subtends a central angle of 225° 
Maths
Find the length of an arc of a circle of radius 5.6cm which subtends an angle of 60°at the centre of the circle take pie 22 \7 
Maths
Find the length of an arc of a circle of radius 5.6cm which subtends an angle of 60°at the centre of the circle of the circle take pie 22 divided by 7