# Thread: Finding angles in a triangle and a circle.

1. ## Finding angles in a triangle and a circle.

If triangle ABC, if A=102 degrees, a=5, and b=2, find C to the nearest degree.
a.23 degrees
b. 55 degrees
c. 62 degrees
d. no exist

2. The radius of a circle is 3.6 cm. The length of the arc of the cirlce cut by a central angle is 8.4 cm. Find the measurement of the central angle,
a.2.3 degrees
b.124.1 degrees
c. 133.7 degrees
d.172.8 degrees

2. 1) Have you recently studied the Law of Signs and Law of Cosines? These could be very useful, here.

2) Diameter = 2*pi*r

8.4 cm / Diameter = How many degrees of the circle?

You should have a theorem about the measure of inscribed angles. Something about "half" comes to mind.

Let's see what you get.

*EDIT: Are you sure that said "central" angle the first time? Sleep reading again, I guess.

3. For the first one, use the law of cosines to find the side length c. Then use the law of sines to find the angle C.

For your second question, I'll let you know a formula.

S=rθ

S is the arc length, r is the radius, and θ is the central angle in radians.