SOLUTION: a wedged-shaped piece is cut from a circular pizza. the radius of the pizza is 6 inches. the rounded edge of the cust of the piece measuures 4.2 inches. to the nearest tenth the an

Question 616846: a wedged-shaped piece is cut from a circular pizza. the radius of the pizza is 6 inches. the rounded edge of the cust of the piece measuures 4.2 inches. to the nearest tenth the angle of the pointed end of the pizza in radians is ?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The keyys to solving this problem:

The "pointed end" of the pizza slice will the the center of the circle. An angle whose vertex is at the center of a circle is called a central angle.
Once we know that the angle is a central angle we can use the fact that the ratio of the angle to the whole circle, radians, is equal to the ratio of the angle's arc to the circumference of the whole circle.

First let's write expressions for the numerator and denominator of each ratio:
The angle is unknown so let's call that x.
The radians for the whole circle is .
The angle's arc is given to us: 4.2 inches.
The circumference of the whole circle is

We can now write an equation we can solve:

We can get x by itself by just multiplying each side by :

which simplifies as follows:

So the angle is 0.7 radians.
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