Answer
We can see that the index of refraction of water is approximately 1.3
Work Step by Step
We can use Snell's law to find an expression for the index of refraction of water $n_2$:
$n_2~sin~\theta_2 = n_1~sin~\theta_1$
$n_2 = \frac{1.00~sin~\theta_1}{sin~\theta_2}$
$n_2 = \frac{sin~\theta_1}{sin~\theta_2}$
We can use Snell's law to find the index of refraction of water for each data pair:
$n_2 = \frac{sin~10^{\circ}}{sin~8^{\circ}} = 1.25$
$n_2 = \frac{sin~20^{\circ}}{sin~15.5^{\circ}} = 1.28$
$n_2 = \frac{sin~30^{\circ}}{sin~22.5^{\circ}} = 1.31$
$n_2 = \frac{sin~40^{\circ}}{sin~29^{\circ}} = 1.33$
$n_2 = \frac{sin~50^{\circ}}{sin~35^{\circ}} = 1.34$
$n_2 = \frac{sin~60^{\circ}}{sin~40.5^{\circ}} = 1.33$
$n_2 = \frac{sin~70^{\circ}}{sin~45.5^{\circ}} = 1.32$
$n_2 = \frac{sin~80^{\circ}}{sin~50^{\circ}} = 1.29$
We can see that the index of refraction of water is approximately 1.3
