We can apply the Law of Cosines to find the measure of this angle, which we will call :

$\displaystyle c^{2} = a^{2} + b^{2} -2ab \cos C$

The widest angle will be opposite the side of length 22, so we will set:

$\displaystyle c=22$, $\displaystyle a=12$, $\displaystyle b=17$

$\displaystyle 22^{2} = 12^{2} + 17^{2} -2\cdot 12\cdot 17 \cos C$

$\displaystyle 484 = 144 + 289 -408 \cos C$

$\displaystyle 51= -408 \cos C$

$\displaystyle \cos C = -\frac{51}{408} = -0.125$

$\displaystyle C = \cos^{-1} 0.125 = 97.2^{\circ }$

By the Law of Cosines:

$\displaystyle \left ( BC\right )^{2} = \left ( AB\right )^{2} + \left ( AC\right )^{2} - 2 \cdot AB \cdot AC \cdot \cos m \angle A$

or, equivalently,

$\displaystyle BC =\sqrt{ \left ( AB\right )^{2} + \left ( AC\right )^{2} - 2 \cdot AB \cdot AC \cdot \cos m \angle A}$

Substitute:

$\displaystyle BC =\sqrt{ 26^{2} +23^{2} - 2 \cdot 26 \cdot 23 \cdot \cos 66 ^{\circ }}$

$\displaystyle \approx \sqrt{ 676 +529 - 1,196 \cdot 0.4067}$

$\displaystyle \approx \sqrt{ 718.6} \approx 26.8$

The period for $\displaystyle \tan(x)$ is $\displaystyle \pi$. However, if a number is multiplied by $\displaystyle x$, you divide the period $\displaystyle \pi$ by what is being multiplied by $\displaystyle x$. Here, $\displaystyle (1/\pi )$ is being multiplied by $\displaystyle x$. $\displaystyle \pi/(1/\pi )$   equals $\displaystyle \pi^{2}$. 

The range of the function $\displaystyle y= \sin x$ is all numbers between $\displaystyle -1$ and $\displaystyle 1$ (the sine wave never goes above or below this).

Of the choices given, $\displaystyle \frac{3}{2}$ is greater than $\displaystyle 1$ and thus not in this range.

When working with basic trigonometric identities, it's easiest to remember the mnemonic: $\displaystyle SOHCAHTOA$.

$\displaystyle \sin=\frac{opposite}{hypotenuse}$

$\displaystyle \cos=\frac{adjacent}{hypotenuse}$, 

$\displaystyle \tan=\frac{opposite}{adjacent}$  

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

One can draw a right triangle with acute angles $\displaystyle \angle x$ and $\displaystyle \angle y$. The side adjacent to $\displaystyle \angle y$ is 4, and the side adjacent to $\displaystyle \angle x$  is 3.  

$\displaystyle tan(x)=\frac{opposite}{adjacent}$ 

To convert we use a common conversion amount. It may be easiest to remember the full circle example. In degrees, a full circle is $\displaystyle 360^{\circ}$ around. In terms of radians, a full circle is $\displaystyle 2\pi$. So to get our answer

$\displaystyle 0.7854\ \text{Radians} *\frac{360^{\circ}}{2\pi\ \text{Radians}}= 45^{\circ}$

To convert from degrees to radians, one multiplies by $\displaystyle \frac{\pi }{180}$.

$\displaystyle 120\cdot \frac{\pi }{180}=\frac{2\pi}{3}$

On the unit circle, (0,-1) is the point that falls between the third and fourth quadrant.  This corresponds to $\displaystyle \frac{3\pi }{2}$.