+0

# trig and segment

0
303
1 thank you

Jun 17, 2019

#1
+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
+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?

hectictar Jun 17, 2019