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demij
17.01.2021 •
Mathematics
A circle with a radius of 15 yards contains a sector with an area of 609 yde. Find the measure of
the central angle of the sector in both radians and degrees.
(HELP PLEASE)(WILL GIVE BRAINLIEST)
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Ответ:
310.3° or 5.41 radians.
Step-by-step explanation:
The area of a circle of radius R is calculated as:
A = pi*R^2
Now, if we have a sector of an angle θ degrees, the area of that sector is:
A = (θ/360°)*pi*R^2
In this case, we know that:
R = 15yd
And the area of the sector is 609 yd^2
Then we can replace these two values in the equation to get:
609yd^2 =(θ/360°)*3.14*(15yd)^2
(609yd^2)*360°/(3.14*(15yd)^2) = θ = 310.3°
And we want the angle also in radians.
We know that:
3.14 rad = 180°
(3.14 rad/180°) = 1
Then:
310.3° = 310.3°*(3.14 rad/180°) = (310.3°/180°)*3.14 rad = 5.41 radians.
Ответ:
The measure of the central angle in degrees and radians are 310.32° and 5.42 rad respectively
Sector of a circle:Area = ∅/360 × πr²where
r = radius
∅ = central angles
Therefore,
609 = ∅ / 360 × 3.14 × 15²
609 = 706.5∅ / 360
219240 = 706.5∅
∅ = 219240 / 706.5
∅ = 310.318471338
∅ = 310.32°
1° = 0.0174533 rad
310.32° = ?
Angle in radian = 310.32° × 0.0174533 = 5.41610573 ≈ 5.42 rad
learn more on circles here; link
Ответ:
1.1
1.01 x 1.1 = 1.111
I hope this is good enough: