SOLUTION: http://s1118.photobucket.com/albums/k608/OddBlackAngel/?action=view&current=ExamFigure7.jpg 1) What is the angle between the tangents at T? A. 30 degrees B. 60 degrees C. 75

Question 540603: http://s1118.photobucket.com/albums/k608/OddBlackAngel/?action=view¤t=ExamFigure7.jpg
1) What is the angle between the tangents at T?
A. 30 degrees
B. 60 degrees
C. 75 degrees
D. 90 degrees
2) How long is arc ACB if the radius of the circle is 6? Round your answer to two decimal places.
A. 6.29
B.12.57
C.18.86
D.25.13
3) How many radians are contained in the angle AOT? Round your answer to three decimal places.
A. .459
B..955
C.1.047
D.2.178

Found 2 solutions by Alan3354, fcabanski:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The link won't work.

Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
1) 60 degrees, B. The radius of a circle drawn to the point any tangent touches the circle is perpendicular. The angle between the tangent and that radius is 90 degrees. In each of those triangles, OAT and OBT one angle is 60, the second is 90, and thus the third in each (angles ATO and BTO) is 30. The angle between the tangents is made up of ATO and BTO, so it is 30 * 2 = 60 degrees.

2) The ratio between the angle that makes up the arc and 360 is the same as the ratio between the arc length and the entire circumference.

C=2*pi*r = 2*(3.14)*6 = 37.7

The arc is 360 - 2*60 = 360-120=240

So the arc length is found with the ratios

Cross multiply.

360x = 37.7*240

Divide both sides by 360

x = 37.7*240/360 = appox. 25.13 (D.)

3) AOT is 60 degrees. Convert degrees to radians by multiplying by pi/180

60*pi/180 = 1.047 (C)

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