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Find the length of $$AB$$ in cm

In the given figure; $$BC= 15$$ cm  and $$\displaystyle \sin B= \frac{4}{5}$$.
The measure of $$AC$$ in cm is

If in given figure $$AD= 2$$ cm, then value of $$AB$$ ( in cm )  is 

The length of $$AD$$ (in cm.) is

Find $$PQ$$, if $$\displaystyle AB = 150\ m, \angle P = 30^{\circ}$$ and $$\displaystyle \angle Q = 45^{\circ}$$

In the given figure, $$\displaystyle \angle B = 60^{\circ}, \angle C =30^{\circ}, AB=8\ cm$$ and $$\displaystyle BC=25\ cm$$. 

Find :

$$(1+tan \alpha \ tan\beta)^2+(tan\alpha -tan\beta)^2$$ is equal to

$$6(sin^6\theta+cos^6\theta)-9(sin^4\theta+cos^4\theta)$$ is equal to

If $$\sin x+\sin^2x+\sin^3x=1$$, then $$\cos^6x-4\cos^4x+8 \cos^2x$$ is equal to