A pendulum is 15.7 cm long, and the bob at the end of the pendulum travels 10.5 cm. Find the degree measure of the angle through which the p

We assume the pendulum bob travels along an arc of a circle of radius 15.7cm.  The angle (in radians) is simply the distance travelled along the arc divided by the radius.  Angle = 10.5/15.7 radians 

$${\mathtt{Angle}} = {\frac{{\mathtt{10.5}}}{{\mathtt{15.7}}}} = {\mathtt{Angle}} = {\mathtt{0.668\: \!789\: \!808\: \!917\: \!197\: \!5}}$$

To get the angle in degrees:

$${\mathtt{Angleindegrees}} = \left({\frac{{\mathtt{10.5}}}{{\mathtt{15.7}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{180}}}{{\mathtt{\pi}}}}\right) = {\mathtt{Angleindegrees}} = {\mathtt{38.318\: \!833\: \!432\: \!316\: \!201\: \!9}}$$