A = 14°
Step-by-step explanation:
We can use sine law in this situation, where
[tex]\dfrac{\sin A}{a} =\dfrac{\sin B}{b}[/tex]
where a and b are the lengths of the sides opposite the corresponding angles. From the given diagram, we can see that
[tex]\dfrac{\sin A}{7\:\text{yd}} = \dfrac{\sin 75°}{28\:\text{yd}}[/tex]
or
[tex]\sin A = \dfrac{7}{28}\sin 75° = 0.241[/tex]
Solving for the angle A, we get
[tex]A = \sin^{-1}(0.241) = 14°[/tex]
