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Igoryamba
3 years ago
6

In the circle below, DB = 22 cm, and m<DBC = 60°. Find BC. Ignore my handwriting.​

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0

Answer:

BC=11\ cm

Step-by-step explanation:

step 1

Find the measure of the arc DC

we know that

The inscribed angle measures half of the arc comprising

m\angle DBC=\frac{1}{2}[arc\ DC]

substitute the values

60\°=\frac{1}{2}[arc\ DC]

120\°=arc\ DC

arc\ DC=120\°

step 2

Find the measure of arc BC

we know that

arc\ DC+arc\ BC=180\° ----> because the diameter BD divide the circle into two equal parts

120\°+arc\ BC=180\°

arc\ BC=180\°-120\°=60\°

step 3

Find the measure of angle BDC

we know that

The inscribed angle measures half of the arc comprising

m\angle BDC=\frac{1}{2}[arc\ BC]

substitute the values

m\angle BDC=\frac{1}{2}[60\°]

m\angle BDC=30\°

therefore

The triangle DBC is a right triangle ---> 60°-30°-90°

step 4

Find the measure of BC

we know that

In the right triangle DBC

sin(\angle BDC)=BC/BD

BC=(BD)sin(\angle BDC)

substitute the values

BC=(22)sin(30\°)=11\ cm

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