$$
I_{f}=0.55 {rm W/m^{2}}
$$

$$
theta=left(90text{textdegree}-35text{textdegree}right)=55text{textdegree}
$$

Unknown:

$$
I_{i}=?
$$

Solution:

We know $I_{f}=I_{i}cos^{2}theta$

So we have

$$
I_{i}=frac{I_{f}}{cos^{2}theta}=frac{left(0.55 {rm W/m^{2}}right)}{cos^{2}55text{textdegree}}=1.7 {rm W/m^{2}}
$$

So we have

$$
I_{f}=I_{i}cos^{2}theta
$$

or

$$
cos^{2}theta=frac{I_{f}}{i_{i}}=frac{1}{2}
$$

so

$$
costheta=frac{1}{sqrt{2}}
$$

or

$$
theta=cos^{-1}left(frac{1}{sqrt{2}}right)=45text{textdegree}
$$