+9466 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?
+9466 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?
