Answer
$4002~miles $
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
$\sin 76.6^{\circ}= \dfrac{a}{a+112}$
This gives: $ a =\dfrac{112 \times \sin 76.6^{\circ}}{1- \sin 76.6^{\circ}}$
or, $ a=4002~miles $
