Question

Consider circle O below. The length of arc BA is 8.4 cm and the length of the radius is 8 cm. The measure of angle AOC is 45°. Circle O is shown. Line segments B O, A O and C O are radii with length 8 centimeters. The length of arc B A is 8.4 centimeters. Angle A O C is 45 degrees. Rounded to the nearest whole degree, what is the measure of angle BOA? ° Rounded to the nearest tenth of a centimeter, what is the length of arc BAC? cm

Answer 1

i) 60°

ii) 14.7 cm

Explanation:

length of Arc BA = 8.4 cm

length of radius = 8 cm

angle AOC = 45°

BO = AO = CO = 8 cm

i) What is the measure of Angle BOA

= length of Arc BA / Radius

= 8.4 / 8 = 1.05 radians = 60.16° ≈ 60°

ii) what is the length of arc BAC

= radius * angle BAC *
`\pi /180`

angle BAC = angle AOC + angle BOA

= 45° + 60° = 105°

hence length of arc BAC

= 8 * 105 *
`\pi /180`

≈ 14.7 cm