We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
139
1
avatar

thank you

 Jun 17, 2019

Best Answer 

 #1
avatar+8810 
+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+8810 
+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

11 Online Users