I tried solving the following question using my little knowledge of law of sines.
HERE IT IS:
A) Find AB
B) Find the measure of OBTUSE angle BAC correct to the nearest tenth of a degree.
HERE IS WHAT I KNOW ABOUT CIRCLE O:
CDB is a secant on circle O.
AB is a tangent on circle O.
BD = 12, CD = 15 and angle AD = 60 degrees
I will use d to represent degrees.
MY WORK:
Angle C = 1/2(angle AD or 60d)
Angle C = 30d
NEXT:
I found the measure of arcs CD and AC by doing this:
arc CD + arc AC + 60d = 360d
Thus, arc CD = 150d = arc AC
Am I right thus far?
I then needed to find angle B, which lies OUTSIDE circle O.
I found angle B to be 45d.
I then used the law of sines to find length AB.
AB/sin30d = 15/sin45d OR sin 135d, right?
I found AB = 10.61
Book's answer is: AB = 18
Knowing that I also need OBTUSE angle BAC, this is what I did:
Angle BAC = 180d - 45d - 30d
Angle BAC = 105d
Book's answer is: 48.6d
Now, 48.6 degrees is NOT obtuse, right?
What did I do wrong?
HERE IT IS:
A) Find AB
B) Find the measure of OBTUSE angle BAC correct to the nearest tenth of a degree.
HERE IS WHAT I KNOW ABOUT CIRCLE O:
CDB is a secant on circle O.
AB is a tangent on circle O.
BD = 12, CD = 15 and angle AD = 60 degrees
I will use d to represent degrees.
MY WORK:
Angle C = 1/2(angle AD or 60d)
Angle C = 30d
NEXT:
I found the measure of arcs CD and AC by doing this:
arc CD + arc AC + 60d = 360d
Thus, arc CD = 150d = arc AC
Am I right thus far?
I then needed to find angle B, which lies OUTSIDE circle O.
I found angle B to be 45d.
I then used the law of sines to find length AB.
AB/sin30d = 15/sin45d OR sin 135d, right?
I found AB = 10.61
Book's answer is: AB = 18
Knowing that I also need OBTUSE angle BAC, this is what I did:
Angle BAC = 180d - 45d - 30d
Angle BAC = 105d
Book's answer is: 48.6d
Now, 48.6 degrees is NOT obtuse, right?
What did I do wrong?