Finding the Area of a Sector using Trigonometric Functions

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In summary, the formula for finding the area of sector FEH is (θ/360) x πr², where θ is the central angle in degrees and r is the radius of the circle. The central angle (θ) can be determined by dividing the arc length of the sector by the radius of the circle and then multiplying by 360 degrees. This same formula can be used for any sector as long as the central angle and radius are known. The unit for the area of sector FEH will depend on the units used for the radius, and there is a simplified version of the formula using the approximate value of π as 3.14.
  • #1
chwala
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Homework Statement
See attached
Relevant Equations
Area of sector
My interest is on part (c) only.

1648079111365.png


Wow, this was a nice one! boggled me a little bit anyways; my last steps to solution,
##A= \dfrac{1}{2} ×16.8319^2 × 0.5707=80.84cm^2## bingo!
Any other approach apart from using sine?
Cheers guys
 
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  • #2
chwala said:
Any other approach apart from using sine?

Yes ! Using the cosine of angle FEH (which happens to be the sine of 1 radian, but that may well be a coincidence :smile: )

Your calculator needs new batteries: not 80.84 but 80.83 :wink: !

##\ ##
 
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Question 1: What is the formula for finding the area of a sector?

The formula for finding the area of a sector is (θ/360) x πr², where θ is the central angle and r is the radius of the circle.

Question 2: How do you find the central angle of a sector?

The central angle of a sector can be found by dividing the arc length of the sector by the radius of the circle.

Question 3: Can the area of a sector be greater than the area of the entire circle?

No, the area of a sector can never be greater than the area of the entire circle. The area of a sector is always a fraction of the area of the circle.

Question 4: What unit of measurement is used for the area of a sector?

The area of a sector is typically measured in square units, such as square inches or square centimeters.

Question 5: Can the area of a sector be negative?

No, the area of a sector cannot be negative as it represents a physical quantity and cannot have a negative value.

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