Year 12 Maths Mechanics - Projectile motion = range of angle - I got the full working out but I don't know how to conclude the final answer

Question

I did the full working out for the following question (images attached below) but I don't know how to explain that the final answer is angles between the two angles 79.3 and 43.7 I've found. (The reason why I know this is the correct answer is because I have looked at the solution, I actually vaguely understand why lol) Could someone please explain to me why the answer is like that and what should i write at the end to validate my answer? Also is it always the case that the range of angles is always between the two angles I can find using the same tactic like above? Thank you so much for your help!

Here is the answer handwritten by my teacher

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Answer 1

Sometimes a picture worth more than thousand words in explanatory power.

Above picture illustrates what happens when you throw a ball towards the building.

• When $4^\circ \le \theta \le 43^\circ$ (the red trajectories), the ball hit the front face of the building.
• When $44^\circ \le \theta \le 79^\circ$ (the green trajectories), the ball fly over the top of the roof. It will either land on top of the roof or behind the building.
• When $80^\circ \le \theta$ (the blue trajectories), the ball doesn't haven't enough time to travel horizontally before it either hit the ground or front face of building (when $\theta \sim 80^\circ$).

All of these is embedded in the math you have worked out, you just need to visualize the trajectories of the ball at different throwing angles.