Answer
$\color{blue}{\approx 2.429 \text{ radians}}$
Work Step by Step
RECALL:
(1) $1^0=60'$
(2) To convert an angle in degrees to radians, multiply $\dfrac{\pi}{180^o}$ then simplify.
Convert $10'$ to degrees to obtain:
$10' = 10' \cdot \dfrac{1^o}{60'} = \dfrac{1}{6}^o$
Thus, the given measurement is equivalent to:
$139\frac{1}{6}^o$
Convert to radians using the formula in (2) above to obtain:
$\require{cancel}
139\frac{1}{6}^o
\\= 139\frac{1}{6}^o \cdot \dfrac{\pi}{180^o}
\\=2.428916542 \text { radians}
\\\color{blue}{\approx 2.429 \text{ radians}}$
