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thank you

 Jun 17, 2019

Best Answer 

 #1
avatar+8966 
+3

a)   We could use the Law of Cosines to find  θ , but since  △ABC  is an isosceles triangle, we can split it into two

      congruent right triangles by drawing a height from  C  to side AB, like this:

 

 

sin( angle )  =  opposite / hypotenuse 
sin( θ/2 )  =  12 / 20

 

 

θ/2  =  arcsin( 12/20 ) 
θ  =  2arcsin( 12/20 )

 

 

θ  ≈  1.287 

 

b)   arc length   =   (radius) * (angle measured in radians)   ≈   (20 cm) * (1.287)   ≈   26 cm

 

c)

       i)   sector area   =   (angle measured in radians)/2 * (radius)2  ≈   (1.287)/2 * (20)2  cm2   ≈   257.4  cm2

 

       ii)  shaded area   =   sector area - triangle area     ...Do you know how to find the area of the triangle?

 Jun 17, 2019
 #1
avatar+8966 
+3
Best Answer

a)   We could use the Law of Cosines to find  θ , but since  △ABC  is an isosceles triangle, we can split it into two

      congruent right triangles by drawing a height from  C  to side AB, like this:

 

 

sin( angle )  =  opposite / hypotenuse 
sin( θ/2 )  =  12 / 20

 

 

θ/2  =  arcsin( 12/20 ) 
θ  =  2arcsin( 12/20 )

 

 

θ  ≈  1.287 

 

b)   arc length   =   (radius) * (angle measured in radians)   ≈   (20 cm) * (1.287)   ≈   26 cm

 

c)

       i)   sector area   =   (angle measured in radians)/2 * (radius)2  ≈   (1.287)/2 * (20)2  cm2   ≈   257.4  cm2

 

       ii)  shaded area   =   sector area - triangle area     ...Do you know how to find the area of the triangle?

hectictar Jun 17, 2019

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