A circle has a chord that goes from #( 5 pi)/4 # to #(5 pi) / 3 # radians on the circle. If the area of the circle is #42 pi #, what is the length of the chord?

Question

How many degrees does the hour hand of a clock turn in 5 minutes?
A circle has a center at #(3 ,1 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,3 )# and passes through #(2 ,7 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,1 )#. What is the length of...
A circle has a center at #(1 ,2 )# and passes through #(4 ,7 )#. What is the length of...

1257 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-07T11:09:28

The length of the chord is #7.89 # unit.

# (5*pi)/4 =225^0 and (5*pi)/3 =300^0 # .

The angle subtended at the center by the chord is

# c= 300-225=75^0# . The area of the circle is

#A_c=42*cancelpi = cancelpi *r^2 :. r^2 = 42 , r =sqrt 42#

We know , chord length # l_c = 2*r * sin (c/2) # or

#l_c= 2 *sqrt42 *sin (75/2) ~~ 7.89(2dp)# unit

The length of the chord is #7.89(2dp) # unit [Ans]