Answer:
15.0
Step-by-step explanation:
Let's start by looking at triangle ORQ. Since RQ is tangent to the circle, we know that angle ∠ORQ is 90°. Then, since OR is equivalent to the radius of 5, RQ is 5√3, and side OQ is clearly larger than RQ, we can identify this as a 90-60-30 degree triangle. This makes side OQ have a length of 10, and angle ∠QOR, opposite of the second largest side, has the second largest angle of 60°, leaving ∠OQR with an angle of 30°.
The formula for the chord length is 2r*sin(c/2), with c being the angle between the two points on the circle (in this case, ∠QOR=∠NOR).. Our radius is 5, so the length of chord NR is 2*5*sin(60/2)=5, making our answer 5(ON)+5(OR)+5(RN)
You will have a better chance of winning because your chance before you opened the first door was 1/3 (since there was 3 doors) but now, you have 2 doors left, so it is a 50% chance that you will win.
Answer:
A circle with circumference 18 had an arc with 120 central angle.
=> Radius of that circle: R = 18/(2 x pi) = 2.86
=> Length of that arc: L = R x 120 x pi/180 = 2.86 x (2/3) x pi = 5.99
Hope this helps!
:)
