oac is a sector of a circle of radius 8cm, centre O ba and bc are tangents to the circle angle aoc = 120 degrees calculate the area of the shaded region give your answer to 3 significant figures

43.8 cm²

Step-by-step explanation:

1. Split the kite in two and find the length of OB

When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.

Then, use the sine rule we can find out the length of OB. It goes like this:

2. Calculate the area of the kite

Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of .

×8×16×sin60 =

But as there are two triangles, we duplicate the answer.

2× =

2. Calculate the area of the sector

area of sector =×πr²

×8²π = π

3. Subtract the area of the sector from the area of the kite

- π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)

HOPE THIS WILL HELP YOU :)

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