Answers:
a) ![L=6cm](https://tex.z-dn.net/?f=L%3D6cm)
b)
Step-by-step explanation:
a) The area of the sector of a circle
is given by:
(1)
and
(2)
Where:
![A=27cm^{2}](https://tex.z-dn.net/?f=A%3D27cm%5E%7B2%7D)
is the radius
(3) is the length of arc
is the angle in radians
In this case we have to find the value of
. So, let's begin substituting the known values in (1):
(4)
Isolating
:
(5)
Substituting (5) in (3):
(6)
Solving:
(7) At this point we have
, but we need to find the value of
in order to have the actual value of the length of arc.
Making (1)=(2):
(8)
Isolating
:
(9)
Substituting (7) and (5) in (9):
(10)
Finding
:
(10) Now that we have the value of the radius, we can substitute it in (7) and finally find the value of the ![L](https://tex.z-dn.net/?f=L)
(11)
(12)
b) In this second case we have:
is the length of arc
is the angle in radians
the radius
We have to find the area of the sector
and we will use equations (1) and (2):
(13)
(14)
(15)
(16)
Knowing
:
This is the area of the sector of the circumference.
Answer:
59.66 cm
Step-by-step explanation:
Circumference of a circle = 2πr
π = 3.14
r = radius = 9.5
2 x 3.14 x 9.5 = 59.66 cm
A*b*sin(c) / 2
8*21*sin(68)=77.88 or rounded 77.9
Answer:
42°
Step-by-step explanation:
It is always good to draw a picture to help you. In this case
tan F = 40/44
m∠F = arctan (40/44) = 42°