27 = sqrt(34) sqrt(20) cos(theta)

We can combine the square roots: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$.

$$\sqrt{34} \times \sqrt{20} = \sqrt{34 \times 20} = \sqrt{680}$$

Divide both sides by $\sqrt{680}$:

$$\cos\theta = \frac{27}{\sqrt{680}}$$

$$\sqrt{680} \approx 26.0768$$ $$\cos\theta \approx \frac{27}{26.0768} \approx 1.0354$$

The range of the cosine function is $[-1, 1]$. Since the calculated value for $\cos\theta$ (approximately 1.0354) is greater than 1, there is no real angle $\theta$ that satisfies this equation.

Therefore, there is no real solution for $\theta$.