look at the shaded right-angled triangle on the left
8 is the hypotenuse n a is opposite to the 40-degree angle
by definition, sin = opposite side / hypotenuse
so sin40=a/8
rearranging a=8sin40
Answer:
central angle=18
arc length=2.5 π feet
area of a sector=31.25π square feet
Step-by-step explanation:
Given
wheel radius=25 feet
attached cars=20
Space between cars along the circumference of wheel= 360/20
=18
Finding arc length:
arc length= radius x angle(in radians)
angle in radian = 18 x π/180 = 0.1π radians
arc length = 25 x 0.1π
=2.5π feet
Area of the circle = πr^2
Area of the circle = π(25)^2
Area of the circle = 625π square feet.
As the ratio of the central angle to the full circle angle is proportional to the area of the sector to the complete circle:
central angle/360=area of sector/area of circle
Area of sector= area of circle x 18/360
= 625π(1/20)
=31.25π !
The green peppers do for the first one because that fraction is larger. The second one is the green paint jar because it is only half while the other is more than half. She uses more flour because it is the larger fraction. And the last one you should explain.