If $$\sin \theta = 4 \cos \theta$$, then what is the value of $$\sin \theta \cos \theta$$ ?

Given that,

$$\sin \theta = 4 \cos \theta$$

So,

$$\dfrac{\sin \theta}{ \cos \theta} = 4$$

$$\tan \theta = 4$$

$$\tan \theta=\dfrac{AB}{BC}=\dfrac{4}{1}$$

$$\Rightarrow AB^2+BC^2=AC^2$$

$$\Rightarrow 4^2+1= AC^2$$

$$\Rightarrow \sqrt{17} =AC$$

So

$$\sin \theta=\dfrac{AB}{AC}=\dfrac{4}{\sqrt{17}}$$

$$\cos \theta=\dfrac{BC}{AC}=\dfrac{1}{\sqrt{17}}$$

Now, substituting the values,

$$\sin \theta \cos \theta =\dfrac{4}{\sqrt{17}} \times \dfrac{1}{\sqrt{17}}=\dfrac{4}{17}$$