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vampirchik [111]
3 years ago
5

In the circle shown below, ∠BAC is a central angle, and r is the length of AB.

Mathematics
1 answer:
Bas_tet [7]3 years ago
8 0

Answer:

Ф = the measure of ∠BAC in radians

Step-by-step explanation:

∵ ∠BAC is a central angle

∴ The are of the sector will depended on the length of the radius <em>r </em>and the measure of the central angle <em>Ф</em>

If the measure of Ф in degrees

∴ The area of the sector = Ф°/360° (π r²)

If the measure of Ф in radians

∴ The area of the sector = 1/2 r² Ф

When to change from degree to radian you do that

Ф radian = Ф°/180 × π

∴ Ф/360 π r² = 1/2 <u>(Ф/180 π)</u> r² ⇒ ∵ underline is Ф radian

∴ Area sector = 1/2 r² Ф ⇒ Ф in radians

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